• Home
  • Carlo Alberto Mantica
Carlo Alberto Mantica

Carlo Alberto Mantica
I.I.S. Lagrange, Milano, Italy

Dr

About

90
Publications
27,651
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,268
Citations
Citations since 2016
64 Research Items
1117 Citations
2016201720182019202020212022050100150200250
2016201720182019202020212022050100150200250
2016201720182019202020212022050100150200250
2016201720182019202020212022050100150200250
Introduction
Carlo Alberto Mantica currently works at I.I.S. Lagrange, Milano, Italy. He is also associated to I.N.F.N., section of Milano. Carlo does research in Mathematical Physics. His current project is ' Generalized Robertson-Walker space-times' with applications to Cosmology and f(R) gravity.
Additional affiliations
September 2001 - present
I.I.S. Lagrange Milano, Italy ; also INFN - Istituto Nazionale di Fisica Nucleare
Position
  • Professor

Publications

Publications (90)
Article
Full-text available
The purpose of this research is to investigate how a ρ-Einstein soliton structure on a warped product manifold affects its base and fiber factor manifolds. Firstly, the pertinent properties of ρ-Einstein solitons are provided. Secondly, numerous necessary and sufficient conditions of a ρ-Einstein soliton warped product manifold to make its factor ρ...
Preprint
Full-text available
We study the geometric properties of certain Codazzi tensors fortheir own sake, and for their appearance in the recent theory of Cotton gravity.We prove that a perfect-fluid tensor is Codazzi if and only if the metric is a generalized Stephani universe. A trace condition restricts it to a warped spacetime, as proven by Merton and Derdzi ́nski. We a...
Article
Full-text available
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with the metric tensor, a ve...
Article
Full-text available
Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a λ,n+m-Einstein manifold M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces to...
Preprint
Full-text available
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with a velocity vector field...
Article
Full-text available
A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive...
Preprint
Full-text available
A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive...
Article
Full-text available
The main object of this paper is to characterize the perfect fluid spacetimes if its metrics are Ricci solitons, gradient Ricci solitons, gradient A-Einstein solitons and gradient Schouten solitons.
Article
Full-text available
Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor bij is called compatible with the curvature tensor if bi m K jklm + bj m K kilm + b k m K ijlm = 0. In addition to establishing some known and some new properties of such tensors, we prove that they form a special Jordan algebra, i.e. the symmetrized product of...
Article
The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent...
Article
Full-text available
The simple structure of doubly torqued vectors allows for a natural characterization of doubly twisted down to warped spacetimes, as well as Kundt spacetimes down to PP waves. For the first ones the vectors are timelike, for the others they are null. We also discuss some properties, and their connection to hypersurface orthogonal conformal Killing...
Preprint
Full-text available
The purpose of this article is to study the inheritance properties of Ricci soliton warped product manifolds by their factor manifolds. First, it is proved that being a Ricci soliton is an inheritance property. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we...
Article
Full-text available
In this note, we characterize [Formula: see text] doubly twisted spacetimes in terms of “doubly torqued” vector fields. They extend Bang–Yen Chen’s characterization of twisted and generalized Robertson–Walker spacetimes with torqued and concircular vector fields. The result is a simple classification of [Formula: see text] doubly-twisted, doubly-wa...
Preprint
Full-text available
The simple structure of doubly torqued vectors allows for a natural characterization of doubly twisted down to warped spacetimes, as well as Kundt spacetimes down to PP waves. For the first ones the vectors are timelike, for the others they are null. We also discuss some properties, and their connection to hypersurface orthogonal conformal Killing...
Preprint
Full-text available
In this note we characterize 1+n doubly twisted spacetimes in terms of `doubly torqued' vector fields. They extend Bang-Yen Chen's characterization of twisted and generalized Robertson-Walker spacetimes with torqued and concircular vector fields. The result is a simple classification of 1+n doubly-twisted, doubly-warped, twisted and generalized Rob...
Article
Full-text available
The object of the present paper is to study weakly B symmetric manifolds (WBS)n. At first some geometric properties of (WBS)n(n > 2) have been studied. Finally, we consider (WBS)4 spacetimes. They turn out to be both perfect and imperfect fluids Robertson-Walker space-times : an equation of state is provided in the first case, and in the second the...
Preprint
Full-text available
General properties of vacuum solutions of $f(R)$ gravity are obtained by the condition that the divergence of the Weyl tensor is zero and $f''\neq 0$. Specifically, a theorem states that the gradient of the curvature scalar, $\nabla R$, is an eigenvector of the Ricci tensor and, if it is time-like, the space-time is a Generalized Friedman-Robertson...
Article
Full-text available
We prove that in Robertson–Walker space-times (and in generalized Robertson–Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert–Einstein Lagrangian density F(R,□R,…,□kR)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...
Article
Full-text available
A. Gray presented an interesting O (n) invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what condition(s), does a factor manifold M i , i =...
Preprint
Full-text available
Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor $b_{ij}$ is named `compatible' with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible ten...
Preprint
Full-text available
Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor b ij is named 'compatible' with the curvature tensor if b i m K jklm + b j m K kilm + b k m K ijlm = 0. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetrized product of K-compatible tensors is K-compatib...
Preprint
Full-text available
We prove that in space-times a velocity field that is shear, vorticity and acceleration-free, if any, is unique up to reflection, with these exceptions: generalized Robertson-Walker space-times whose space sub-manifold is warped, and twisted space-times (the scale function is space-time dependent) whose space sub-manifold is doubly twisted. In spac...
Article
Full-text available
We prove that in space-times a velocity field that is shear, vorticity and acceleration-free, if any, is unique up to reflection, with these exceptions: generalized Robertson-Walker space-times whose space sub-manifold is warped, and twisted space-times (the scale function is space-time dependent) whose space sub-manifold is doubly twisted. In spac...
Preprint
Full-text available
We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian density $F(R,\square R, ... , \square^k R)$ have the form of perfect fluids in the field equations. This statement d...
Preprint
Full-text available
We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian density F (R, R, ..., k R) have the form of perfect fluids in the field equations. This statement definitively allow...
Preprint
Full-text available
In this paper, it is proved that the factor manifolds M i , i = 1, 2 of a doubly warped product manifold M = f 2 M 1 × f 1 M 2 acquire the Einstein-like class type A, B, P, I ⊕ B, I ⊕ A, or A ⊕ B of M by imposing a sufficient condition on the warping functions in each case. As an application, Einstein-like doubly warped product spacetimes of type A...
Article
Full-text available
In an-dimensional Friedmann-Robertson-Walker metric, it is rigorously shown that any analytical theory of gravity f(R,G), where R is the curvature scalar and G is the Gauss-Bonnet topological invariant, can be associated to a perfect-fluid stress-energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometricall...
Preprint
Full-text available
In an $n$-dimensional Friedmann-Robertson-Walker metric, it is rigorously shown that any smooth theory of gravity $f(R,{\cal G})$, where $R$ is the curvature scalar and $\cal G$ is the Gauss-Bonnet topological invariant, can be associated to a perfect-fluid stress-energy tensor. In this perspective, dark components of the cosmological Hubble flow c...
Preprint
Full-text available
We prove that in space-times a velocity field that is shear, vorticity and acceleration-free is unique, up to reflection, with these exceptions: warped space-times whose space sub-manifold is warped, and twisted space-times (the scale function is space-time dependent) whose space sub-manifold is doubly twisted. In space-time dimension n = 4, the Ri...
Preprint
Full-text available
In this paper, it is proved that the factor manifolds $M_{i},i=1,2$ of a doubly warped product manifold $M=_{f_{2}}M_{1}\times _{f_{1}}M_{2}$ acquire the Einstein-like class type $\mathcal{A},$ $\mathcal{B}$ or $\mathcal{P}$ of $M$ by imposing a sufficient condition on the warping functions in each case. Einstein-like doubly warped product space-ti...
Preprint
Full-text available
In this paper, it is proved that the factor manifolds M i , i = 1, 2 of a doubly warped product manifold M = f 2 M 1 × f 1 M 2 acquire the Einstein-like class type A, B or P of M by imposing a sufficient condition on the warping functions in each case. Einstein-like doubly warped product spacetimes are considered.
Preprint
Full-text available
The Ricci tensor of a Robertson-Walker space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein's equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, th...
Article
Full-text available
We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray’s decomposition of the gradient of the Ricci tensor. In all but one, the Ricci tens...
Article
Full-text available
In this note we show that Lorentzian Concircular Structure manifolds (LCS)n coincide with Generalized Robertson-Walker space-times.
Article
Full-text available
The Ricci tensor of a Robertson-Walker space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein's equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words,the...
Preprint
Full-text available
The Ricci tensor of a Robertson-Walker space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein's equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, th...
Preprint
Full-text available
We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In all but one, the Ricci tens...
Preprint
Full-text available
We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In all but one, the Ricci tens...
Article
Full-text available
We show that an n-dimensional generalized Robertson-Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress-energy tensor for any f(R) gravity model. Furthermore we prove that a conformally flat GRW space- time is still a perfect fluid in both f(R) and quadratic gravity where other curvature invariant...
Preprint
Full-text available
We show that an n-dimensional generalized Robertson-Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress-energy tensor for any f(R) gravity model. Furthermore we prove that a conformally flat GRW space- time is still a perfect fluid in both f(R) and quadratic gravity where other curvature invariant...
Preprint
Full-text available
We show that an n-dimensional generalized Robertson-Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress-energy tensor for any f (R) gravity model. Furthermore we prove that a conformally flat GRW space-time is still a perfect fluid in both f (R) and quadratic gravity where other curvature invarian...
Article
Full-text available
In our paper “A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field”.
Conference Paper
Full-text available
We show that an n-dimensional generalized Robertson-Walker space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress-energy tensor in any f(R) theory of gravitation
Article
Full-text available
We prove that, in a space-time of dimension n > 3 with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant di- vergence of the Weyl tensor is zero if the contraction of the Weyl tensor with the velocity is zero. The other way, if the covariant divergence of the Weyl tensor is zero, then the contraction of the We...
Article
Full-text available
We extend to twisted space-times the following property of Generalized Robertson-Walker spacetimes: the Weyl tensor is divergence-free if and only if its contraction with the time-like unit torse-forming vector is zero. Despite the simplicity of the statement, the proof is involved. As a product of the same calculation, we introduce a new generaliz...
Article
We show that n-dimensional perfect fluid spacetimes with divergence- free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under...
Article
Full-text available
We show that n-dimensional perfect fluid spacetimes with divergence- free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under...
Article
Full-text available
We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statement recalls the "shear-free conj...
Article
Full-text available
We show that in dimension n>3 the class of simple conformally recurrent space-times coincides with the class of conformally recurrent pp-waves.
Article
Full-text available
In this paper, it is proved that the fiber manifold M2M2 of a warped product manifold M=M1×fM2M=M1×fM2 inherits the Einstein-like class type of MM whereas the base manifold does under some conditions. Some related results are considered. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219887817501663
Article
Full-text available
In this paper, we introduce a new tensor named (Formula presented.)-tensor which generalizes the (Formula presented.)-tensor introduced by Mantica and Suh [Pseudo (Formula presented.) symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. Then, we study pseudo-(Formula presented.)-symm...
Article
Full-text available
Robertson-Walker and Generalized Robertson-Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the existence of such (unique) vector field, with no other constrain. Twisted manifolds generalize RW and GRW spacetime...
Article
Full-text available
Generalized Robertson-Walker spacetimes extend the notion of Robertson-Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization in terms of a timelike concircular vector. Together with their most important properties, some new results are presented.
Article
Full-text available
In this paper, we study the properties of weakly conformally symmetric pseudo- Riemannian manifolds focusing particularly on the (Formula presented.)-dimensional Lorentzian case. First, we provide a new proof of an important result found in literature; then several new others are stated. We provide a decomposition for the conformal curvature tensor...
Article
We study the properties of weakly conformally symmetric pseudo-Riemannian manifolds, with particular emphasis on the 4-dimensional Lorentzian case. We provide a decomposition of the conformal curvature tensor in dimensions n ≥ 5. Moreover, some identities involving two particular covectors are stated; for example it is proven that under certain con...
Article
Full-text available
We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension $n\ge 3$. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid term plus a term linear in the contracted Weyl tensor. The Weyl tensor is harmonic if and only if it is annihil...
Article
Full-text available
Extended recurrent pseudo-Riemannian manifolds were introduced by Mileva Prvanovic'. We reconsider her work in the light of recent results and show that the manifold is conformally flat, and it is a space of quasi-constant curvature. We also show that an extended recurrent Lorentzian manifold, with time-like associated covector, is a perfect fluid...
Article
Full-text available
The object of the present paper is to study weakly cyclic Z symmetric spacetimes. At first we prove that a weakly cyclic Z symmetric spacetime is a quasi Einstein spacetime. Then we study \({{(WCZS)}_{4}}\) spacetimes satisfying the condition div \({C=0}\). Next we consider conformally flat \({{(WCZS)}_{4}}\) spacetimes. Finally, we characterise du...
Article
Full-text available
A generalized Robertson–Walker (GRW) space-time is the generalization of the classical Robertson–Walker space-time. In the present paper, we show that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a GRW space-time. Further, we show that a stiff matt...
Article
Full-text available
Conformally recurrent pseudo-Riemannian manifolds of dimension n ≥ 5 are investigated. The Weyl tensor is represented as a Kulkarni–Nomizu product. If the square of the Weyl tensor is non-zero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the trac...
Article
Full-text available
In this paper we present some new results about n(≥4)-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a co...
Article
In this paper we present some new results about n(≥ 4)-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a c...
Article
Full-text available
A perfect-fluid space-time of dimension n ≥ 4, with (1) irrotational velocity vector field and (2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with an Einstein fiber. Condition (1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the ve...
Research
Full-text available
perfect-fluid space-time of dimension n> �4 with irrotational velocity �eld and null divergence of theWeyl tensor is a generalised Robertson- Walker space. The first condition is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity �field is zero.
Research
Full-text available
A perfect-fuid space-time of dimension n �> 4 with irrotational velocity �eld and null divergence of the Weyl tensor is a generalised Robertson- Walker space. The �first condition is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity �field is zero.
Article
Full-text available
The object of the present paper is to study weakly cyclic Z symmetric manifolds. Some geometric properties have been studied. We obtain a sufficient condition for a weakly cyclic Z symmetric manifold to be a quasi Einstein manifold. Next we consider conformally flat weakly cyclic Z symmetric manifolds. Then we study Einstein (WCZS)n (n > 2). Also w...
Article
Full-text available
Conformally recurrent pseudo-Riemannian manifolds of dimension n � 5 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak’s theorem, the explicit expression of the trace...
Article
Full-text available
The object of the present paper is to determine the nature of the associated 1-forms of a weakly symmetric manifold.
Article
Full-text available
Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor may be represented as a Koulkarni-Nomizu product involving a symmetric tensor and the recurrence vector. If the recurrence vector is a closed form, the Ricci and two other tensors are Weyl compatible. If the recurrence vector is non-null, a covarian...
Article
Full-text available
We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications. In particular, it is shown that the existence of a Weyl compatible vector implies that the Weyl tensor is algeb...
Article
Full-text available
In this paper, we introduce the notion of recurrent conformal 2-forms on a pseudo-Riemannian manifold of arbitrary signature. Some theorems already proved for the same differential structure on a Riemannian manifold are proven to hold in this more general contest. Moreover other interesting results are pointed out; it is proven that if the associat...
Article
The object of the present paper is to study weakly cyclic Z symmetric manifolds. Some geometric properties have been studied. We obtain a sufficient condition for a weakly cyclic Z symmetric manifold to be a quasi Einstein manifold. Next we consider conformally flat weakly cyclic Z symmetric manifolds. Then we study Einstein (WCZS)n (n > 2). Also w...
Article
Full-text available
In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field , focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed wi...
Article
Full-text available
Conformally quasi-recurrent (CQR)n pseudo-Riemannian manifolds are investigated, and several new results are obtained. It is shown that the Ricci tensor and the gradient of the fundamental vector are Weyl compatible tensors (the notion was introduced recently by the authors and applies to significative space-times), (CQR)n manifolds with concircula...
Article
Full-text available
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A k is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic par...
Article
Full-text available
In this paper, we introduce a new kind of tensor whose trace is the well-known Z tensor defined by the present authors. This is named Q tensor: the displayed properties of such tensor are investigated. A new kind of Riemannian manifold that embraces both pseudo-symmetric manifolds (PS)n and pseudo-concircular symmetric manifolds (CS)n is defined. T...
Article
Full-text available
In this paper we recall the closedness properties of generalized curvature 2-forms, which are said to be Riemannian, Conformal, Projective, Concircular and Conhar- monic curvature 2-forms, given in [?]. Moreover, we extend the concept of recurrent generalized curvature tensor to the associated curvature 2-forms while generalizing some known results...
Article
In this paper, we introduce a new kind of Riemannian manifold that generalize the concept of weakly Z-symmetric and pseudo-Z-symmetric manifolds. First a Z form associated to the Z tensor is defined. Then the notion of Z recurrent form is introduced. We take into consideration Riemannian manifolds in which the Z form is recurrent. This kind of mani...
Article
Full-text available
In this paper we introduce a new notion of Z-tensor and a new kind of Riemannian manifold that generalize the concept of both pseudo Ricci symmetric manifold and pseudo projective Ricci symmetric manifold. Here the Z-tensor is a general notion of the Einstein gravitational tensor in General Relativity. Such a new class of manifolds with Z-tensor is...
Article
Full-text available
Derdziński and Shen's theorem on the restrictions on the Riemann tensor imposed by existence of a Codazzi tensor holds more generally when a Riemann compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity for a new “Codazzi deviation tensor”, with a...
Article
Full-text available
We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named weakly Z-symmetric and is denoted by (WZS) n . If the Z tensor is singular we give conditions for the existence of a proper concircular...
Article
Full-text available
Abstract: We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.
Article
Full-text available
We extend a classical result by Derdzinski and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms) as well as tensors with gauged Codazzi condition (i.e. "recurrent 1-forms"), typical of some well known differential s...
Article
Full-text available
A second-order differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed. The new structure of K -recurrency naturally emerge...
Article
Full-text available
In order to give a new proof of a theorem concerned with conformally symmetric Riemannian manifolds due to Roter and Derdzin- sky [8], [9] and Miyazawa [15], we have adopted the technique used in a theorem about conformally recurrent manifolds with harmonic conformal curvature tensor in [3]. In this paper, we also present a new proof of a suc- cess...
Article
A material surface of pure constituents with a flexible molecular chain (amphiphilics) is considered; thermodynamic behaviour is studied in the chain length-temperature plane. The Hamiltonian of the system is modelled as the sum of a formation term which refers to the polymer nature of the chain, and of a fluctuation term with a specific elastic fo...
Article
A covariant second-order differential identity for the Riemann tensor is derived from the Bianchi identities, on a manifold with symmetric connection. MSC class: 53A45, 53B20.

Network

Cited By

Projects

Projects (2)
Project
This project aims at generalization of some curvature conditions on warped product manifolds and their applications on some spacetimes.
Project
General properties of Generalized Robertson-Walker space-times are investigated in term of curvature conditions imposed on the Weyl tensor.