Alexander Pigazzini

• Researcher at Mathematical and Physical Science Foundation (Denmark)

We introduce a novel concept known as the partially negative dimensional product manifold, abbreviated as PNDP-manifold. Specifically, a PNDP-manifold represents a unique form of Einstein sequential warped product manifold, where the base manifold $\mathcal{B}$ is a Riemannian (or pseudo-Riemannian) product manifold expressed as \( \mathcal{B}= \ma...

We address the long-standing problem of the existence of a Riemannian metric on $S^2\times T^2$ with strictly positive biorthogonal curvature ($K_{\text{biort}}(\sigma) > 0 $), but in a weaker framework, by introducing an affine connection with antisymmetric closed torsion, naturally encoded in the cohomology of $S^2 \times T^2$ ($H^3(S^2 \times T^...

This work introduces the G$_2$-Ricci flow on seven-dimensional manifolds with non-zero torsion and explores its physical implications. By extending the Ricci flow to manifolds with G$_2$ structures, we study the evolution of solitonic solutions and their role in spontaneous symmetry breaking in gauge theories. In particular, this model proposes tha...

Symmetry and antisymmetry are fundamental concepts in many strict sciences. Pairwise comparisons (PC) matrices are fundamental tools for representing pairwise relations in decision making. In this theoretical study, we present a novel framework that embeds additive skew-symmetric PC matrices into the Grassmannian manifold $G(2, n)$. This framework...

Physical properties such as shape, volume, and size influence the dynamics of biological systems. In this context, we focus on the geometric properties of limb movements and their physiological and biomechanical effects. Using hand grasping as a paradigmatic example, we describe how dynamic changes in geometric configuration can affect the pathophy...

In this paper, we aim to investigate the properties of an almost $*$-Ricci-Bourguignon soliton (almost $*-$R-B-S for short) on a Kenmotsu manifold (K-M). We start by proving that if a Kenmotsu manifold (K-M) obeys an almost $*-$R-B-S, then the manifold is $\eta$-Einstein. Furthermore, we establish that if a $(\kappa, -2)'$-nullity distribution, whe...

We study a particular type of Einstein warped-product manifold where the warping function must satisfy the homogeneous version of the screened Poisson equation. Under these assumptions, we show that the dimension of the manifold, the (constant negative) Ricci curvature and the screened parameter are related through a quadratic equation.

We study a particular type of Einstein warped-product manifold where the warping function must satisfy the homogeneous version of the screened Poisson equation. Under these assumptions, we show that the dimension of the manifold, the (constant negative) Ricci curvature and the screened parameter are related through a quadratic equation.

We present the proof for the source of exchange flying ring of the biological bosonic state in homochirality of L-amino acids. It is a source of knot in parallel transport of Yang–Mills field in genetic code evolved from natural selection. It serves as a source of protein folding structure in L-amino acids over all the protein structure of a living...

In this paper, we study warped product on generalized quasi-Einstein manifolds with respect to affine connections. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein warped products manifolds with respect to affine connections. Furthermore, it is proved that generalized quasi-Einstein manifold to be a quas...

In this work we will classify physically admissible manifold structures by the use of Waldhausen categories. These categories give rise to algebraic K-Theory. Moreover, we will show that a universal K-spectrum is necessary for a physical manifold being admissible. Application to the generalized structure of D-branes are also provided. This might gi...

In this paper, we present some more fundamental properties of the notion of neutrosophic Lie subalgebra of a Lie algebra. 2020

In this paper we present not only some properties related to bi-warped product submanifolds of locally conformal almost cosymplectic manifolds, but also we show how the squared norm of the second fundamental form and the bi-warped product's warping functions are related when the bi-warped product submanifold has a proper slant submanifold as a base...

In this paper we study on warped...

In this paper, we study the PNDP-manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the Weyl tenso...

In this paper, the first Chen inequality is proved for general warped product submanifolds in Riemannian space forms, this inequality involves intrinsic invariants (δ-invariant and sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer for Chen's Problem 1 relating to establish simple relationships...

We will classify physically admissible manifold structures by the use of Waldhausen categories. These categories give rise to algebraic K-Theory. Moreover, we will show that a universal K-spectrum is necessary for a physical manifold being admissible. Application to the generalized structure of D-branes are also provided. This might give novel insi...

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both...

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both...

In the present paper, we study the PNDP- manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the We...

In the first part of the paper, we try to identify the presence of gravity, at a microscopic level, by introducing conical defects and maintaining an approach that assumes topological equivalence among the underlying manifolds that form the tissue of the D-brane itself. In the second part, we will present an alternative to the conical defects, cons...

We derive the general formulas for a special configuration of the sequential warped-product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a generic diagonal conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a $ n_1 $-dimensional and $...

In this paper, warped product CR-submanifolds in Kähler manifolds and warped product contact CR-submanifolds in Sasakian, Kenmotsu and cosymplectic manifolds, are shown to possess a geometric property; namely D T-minimal. Taking benefit from this property, an optimal general inequality is established by means of the Gauss equation, we leave cosyple...

The aim of this paper is to use a special type of Einstein warped product manifolds recently introduced, the so-called PNDP-manifolds, for the differential geometric study, by focusing on some aspects related to dark field in financial market such as the concept of dark volatility. This volatility is not fixed in any relevant economic parameter, a...

We establish two main inequalities; one for the norm of the second fundamental form and the other for the matrix of the shape operator. The results obtained are for cosymplectic manifolds and, for these, we show that the contact warped product submanifolds naturally possess a geometric property; namely $\mathcal{D}_1$-minimality which, by means of...

We establish two main inequalities; one for the norm of the second fundamental form and the other for the matrix of the shape operator. The results obtained are for cosymplectic manifolds and, for these, we show that the contact warped product submanifolds naturally possess a geometric property; namely D 1-minimality which, by means of the Gauss eq...

In our research work, we study the generlized Cauchy-Riemann lightlike submanifolds of metallic semi-Riemannian manifolds. We establish conditions for integrability of distributions and investigate the geometry of the leaves of distributions.

In this paper we present not only some properties related to bi-warped product submanifolds of locally conformal almost cosymplectic mani-folds, but also we show how the squared norm of the second fundamental form and the bi-warped product's warping functions are related when the bi-warped product submanifold has a proper slant submanifold as a bas...

In this paper, the first Chen inequality is proved for general warped product submanifolds in Riemannian space forms, this inequality involves intrinsic invariants (δ-invariant and sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer for Problem 1. As a geometric application, this inequality is a...

In this paper, warped product CR-submanifolds in Kähler manifolds and warped product contact CR-submanifolds in Sasakian, Kenmotsu and cosymplectic manifolds, are shown to possess a geometric property; namely D T-minimal. Taking benefit from this property, an optimal general inequality is established by means of the Gauss equation, we leave cosyple...

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both...

Recently PNDP-manifolds have been introduced, and these have shown to be useful in applicative aspects especially in the field of cosmology, introducing a new geometric/topological approach to the concept of ”emerging space”. However, the applications considered so far concern only trivial and flat PNDP-manifolds. Therefore we show the existence of...

We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a generic diagonal conformal metrics. Subsequently we study the case in which these two manifolds are conformal to a $n_1$-dimensional and $n_...

The general cone is one of the intersting figures in differential eometry, as a surface of revolution it is indeed a warped product subman-ifolds. This study considers the genral cone in Riemannian manifolds, as a particular case we investigate the well-known cone in space as an an example assering our results. The first part of the paper provides...

In this paper, we introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative-dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the ori-entability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational i...

(Translated version of our interview from RECCOM magazine: https://www.reccom.org/legame-tra-scale-di-energia-diverse-gravita/) A new work just published in Int. J. Geom. Meth. Mod. Phys. Vol. 18, No. 14 (December 2021), entitled "A topological approach for emerging D-Branes and its implications for gravity", continues the search for emerging spac...

In this paper, warped product contact CR-submanifolds in Sasakian, Kenmotsu and cosymplectic manifolds are shown to possess a geometric property ; namely D T-minimal. Taking benefit from this property, an optimal general inequality for warped product contact CR-submanifolds is established in both Sasakian and Kenmotsu manifolds by means of the Gaus...

We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold B is a Remannian (or pseudo-Riemannian) product-manifold B = Π q i=1 B i × Π q i=...

We introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can d...

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of "emergent space" as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole. Finally, in Subsection 2.3, we give a...

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a nonorientable wormhole, but mainly we provide a topological in...

We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold $B$ is a Remannian (or pseudo-Riemannian) product-manifold $B=\Pi_{i=1}^{q'}B_i \...

The main purpose of this paper is to show some interpretative aspects of PNDP theory as geometric/topological approach in the cosmological field, introducing the concept of "emergent" space. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole. Finally, in Subsection 2.3, we...

The aim of this paper is to use a special type of Einstein warped product manifolds introduced by A. Pigazzini et al. in [1], the so-called PNDP-manifolds, for the differential geometric study, of some aspects related to dark field in financial market such as the concept of dark volatility which has been introduced and studied by R. Pincak et al. i...

We study the (2+2)-Einstein warped product manifolds ($M, \bar{g}$), where the scalar curvature of the Base is a multiple of the warping function , and we called this condition (inside a warped product manifold) f-curvature-Base ($R_{f_B}$). The aim of this paper is to check if there are Base-manifolds with non-flat metrics that satisfy this condit...

Differential Geometry - Dynamical System (ISSN 1454-511X) For the studied cases in [11], the author showed that having the f-curvature-base R f B is equal to requiring a flat metric on the base-manifold. In [12] the authors introduced a new kind of Einstein warped product manifold, composed by positive-dimensional manifold and negative-dimensional...

We provide a possible way of constructing new kinds of manifolds which we will call Partially Negative Dimensional Product manifold (PNDP-manifold for short). In particular a PNDP-manifold is an Einstein warped product manifold of special kind, where the base-manifold $B$ is a Remannian (or pseudo-Riemannian) product-manifold $B=\Pi_{i=1}^{q'}B_i \...

For the studied cases in [10], the author showed that having the {\textit {$f$-curvature-Base}} ($R_{f_B}$) is equal to requiring a flat metric on the base-manifold. In [11] the authors introduced a new kind of Einstein warped product manifold, composed by positive-dimensional manifold and negative-dimensional manifold, the so called \textit{PNDP-m...

The aim of this short article is to investigate the possibility of existence of totally umbilical isometric immersions in R^3 with isothermal parametrization and harmonic metric. JP Journal of Geometry and Topology (ISSN: 0972-415X) DOI: http://dx.doi.org/10.17654/GT021030247

The goal of this paper is to analyze surfaces with constant skew curvature (CSkC), and show that the class of CSkC surfaces with non-constant principal curvatures does not contain any Bonnet surfaces. MSC: 53A10 (https://projecteuclid.org/euclid.jgsp/1518577293)

The aim of this short article is to investigate the possibility of existence of totally umbilical isometric immersions in R^3 with isothermal parametrization and harmonic metric.