S. K. Hui

• Ph.D.
• Professor (Full) at University of Burdwan

This article provides a Li–Yau-type gradient estimate for a semilinear weighted parabolic system of semilinear equations along an abstract geometric flow on a smooth measure space. A Harnack-type inequality on the system is also derived at the end.

In this paper, we determine the variation formula for the first eigenvalue of (p,q)-biharmonic system on a closed Riemannian manifold. Several monotonic quantities are also derived.

In this article we derive both Hamilton type and Souplet–Zhang type gradient estimations for a system of semilinear equations along a geometric flow on a weighted Riemannian manifold.

In this paper, we investigate the sectional contravariant curvature of a doubly warped product manifold ( fB×bF,g˜,Π=ΠB+ΠF) equipped with a product Poisson structure Π, using warping functions and sectional curvatures of its factor manifolds (B,g˜B,ΠB) and (F,g˜F,ΠF). Qualar and null sectional contravariant curvatures of ( fB×bF,g˜,Π) are also give...

In this research paper, we determine the nature of conformal [Formula: see text]-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal [Formula:...

The main goal of this research paper is to investigate contact CR-warped product submanifolds within Sasakian space forms, utilizing a semi-symmetric metric connection. We conduct a comprehensive analysis of these submanifolds and establish several significant results. Additionally, we formulate an inequality that establishes a relationship between...

In this article we derive Bernstein type gradient estimation for local weighted heat equation on static weighted Riemannian manifold and evolving weighted Riemannian manifold along local Ricci flow and extended local Ricci flow. We showed that along local Ricci flow and extended local Ricci flow we can derive Bernstein type estimation for weighted...

We began by considering invariant, anti-invariant, proper slant, and pointwise slant submanifolds of a Lorentzian concircular structure manifold. Subsequently, we explored two distinct categories of warped product submanifolds. The first category encompassed the fiber submanifold as an anti-invariant submanifold, while the second category included...

The method of gradient estimation for the heat-type equation using the Harnack quantity is a classical approach used for understanding the nature of the solution of these heat-type equations. Most of the studies in this field involve the Laplace–Beltrami operator, but in our case, we studied the weighted heat equation that involves weighted Laplaci...

This article is devoted to the study of several estimations for a positive solution to a nonlinear weighted parabolic equation on a weighted Riemannian manifold. We therefore derive new Li-Yau type and Hamilton type gradient estimates yielding several consequences. We also derive Hessian estimate and some corollaries for the same equation. Among th...

In this article we derive a Li–Yau-type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold evolving by a geometric flow. As an application, a Harnack-type inequality is also derived in the end.

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level $2$, $2$-quasi Einstein, generalized quasi-Einstein and Roter typ...

In this article, we consider (M n , g(t)) an n-dimensional closed Riemannian manifold whose metric g(t) evolves by the abstract geometric flow and the geometric constant λ b a as the lowest constant such that the equation −∆u + au log u + bSu = λ b a u with M u 2 dµ = 1 has a positive solution, where a (> 0) and b are two real constants. Here we fi...

In this article we derive Hamilton type gradient estimate and Souplet-Zhang type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold evolving by a geometric flow in such a way that the Bakry-?mery Ricci tensor is bounded below.

In this paper we discussed CR-submanifold of SQ-Sasakian manifold. Next, we considered Chaki pseudo parallel as well as Deszcz pseudo parallel CR-submanifold of SQ-Sasakian manifold. Further we studied almost Ricci soliton and almost Yamabe soliton with torse forming vector field on CR-subamnifold of SQ-Sasakian manifold using semi-symmetric metric...

The Bardeen solution corresponding to Einstein field equations with a cosmological constant is a regular black hole. The main goal of this manuscript is to investigate the geometric structures in terms of curvature conditions admitted by this spacetime. It is found that this spacetime is pseudosymmetric and possess several kinds of pseudosymmetries...

The major goal of this work is to express the Ricci curvature inequality for biwarped product submanifold of the type [Formula: see text] isometrically immersed in a Kenmotsu space form via terms of the squared norm of mean curvature vector and warping functions, where [Formula: see text], [Formula: see text] and [Formula: see text] are the slant s...

The objective of this paper is to achieve the inequality for Ricci curvature of a semi-slant warped product submanifold isometrically immersed in a generalized complex space form admitting a nearly Kaehler structure in the expressions of the squared norm of mean curvature vector and warping function. In addition, the equality case is likewise discu...

In this paper we derive the evolution equation of the first nonzero eigenvalue of the (p,q)-Laplace system under the unnormalized Hk-flow. By imposing some conditions on the mean curvature we prove the monotonicity of the first nonzero eigenvalue under the unnormalized Hk-flow.

In this paper, invariant and anti-invariant submanifolds of cosymplectic statistical- space-forms are considered. Among others, a generalized Wintgen inequality on Legendrian submanifolds of such space forms is obtained.

The object of the present paper is to study of Yamabe solitons on generalized (k, µ)-space-forms with respect to semisymmetric metric connection and obtained sufficient conditions for which such Yamabe soliton turns out to be a Yamabe soliton with respect to Levi-Civita connection.

In this paper, we have studied [Formula: see text]-quasi-Einstein spacetimes. Some basic results of such spacetimes are derived. Perfect and viscous fluid [Formula: see text]-quasi-Einstein spacetimes are also studied and the expressions of pressure, cosmological constant and energy density are obtained. We have proved that if the generator [Formul...

The projective flatness in the pseudo-Riemannian geometry and Finsler geometry is a topic that has attracted over time the interest of several geometers. A Finsler space (M, F) is composed by a differen-tiable manifold and a fundamental function F (x, y) = √ a ij (x)y i y j + b i y i , where (x, y) ∈ T M − {0}, where a ij (x) is a Riemannian metric...

The object of the present paper is to study the properties of Ricci and Yamabe solitons on the perfect fluid LP-Sasakian spacetimes. Certain results related to the application of such spacetimes in the general relativity and cosmology are obtained.

The purpose of the present paper is to study semi-generalized recurrent, semi-generalized Ricci recurrent and conformal Ricci soliton on (LCS)n-manifold.

In this paper we have addressed the behaviour of Yamabe constant along the Cotton flow. We have also studied the evolution of ADM mass along the Cotton flow and it is shown that the ADM mass is conserved along the Cotton flow. Among others evolution of Bach tensor under Cotton flow is derived. It is shown that if the metric of a local conformally f...

Recently, Naghi et al. [32] studied warped product skew CR-submanifold of the form M1 xf M? of order 1 of a Kenmotsu manifold ?M such that M1 = MT x M?, where MT, M? and M? are invariant, anti-invariant and proper slant submanifolds of ?M. The present paper deals with the study of warped product submanifolds by interchanging the two factors MT and...

The object of the present paper is to carry out η-Ricci soliton on 3-dimensional regular f-Kenmotsu manifold and we turn up some geometrical results. Furthermore we bring out the curvature conditions for which η-Ricci soliton on such manifolds are shrinking, steady or expanding. We wind up by considering examples of existence of shrinking and expan...

The paper deals with the study of Casorati curvature of submanifolds of generalized (k,μ)-space-form with respect to Levi-Civita connection as well as semisymmetric metric connection and derived two optimal inequalities between scalar curvature and Casorati curvature of such space forms. The equality cases are also considered.

In this paper, we have studied submanifolds especially, totally umbilical submanifolds of generalized \((k,\mu )\)-space-forms. We have found a necessary and sufficient condition for such submanifolds to be either invariant or anti-invariant. It is also shown that every totally umbilical submanifold of a generalized \((k,\mu )\)-space-form is a pse...

The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi–Civita connection as well as semisymmetric metric connection. It is obtained that these two classes are equivalent with a certain condition. In addition, invariant and anti-invariant submani...

Recently, Naghi et al. \cite{NAGHI} studied warped product skew CR-submanifold of the form $M_1\times_fM_\bot$ of order $1$ of a Kenmotsu manifold $\bar{M}$ such that $M_1=M_T\times M_\theta$, where $M_T$, $M_\bot$ and $M_\theta$ are invariant, anti-invariant and proper slant submanifolds of $\bar{M}$. The present paper deals with the study of warp...

The present paper deals with the study of warped product pointwise bi-slant submanifolds of Kenmotsu manifolds with an example. The characterization for such submanifold is also discussed. An inequality of such submanifold is obtained and its equality case is also considered.

The present paper deals with the study of warped product pointwise bi-slant submanifolds of Kenmotsu manifolds with an example. The characterization for such submanifold is also discussed. An inequality of such submanifold is obtained and its equality case is also considered.

The present paper deals with some results of almsot semi-invariant submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.

In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold $M^n$ when the metric is a Yamabe soliton. Using these quantities we have obtained bound on the soliton constant. We have proved that the commutator of two soliton vector fields with the same metric in a given conformal class produces a Killing ve...

In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold $M^n$ when the metric is a Yamabe soliton. Using these quantities we have obtained bound on the soliton constant. We have proved that the commutator of two soliton vector fields with the same metric in a given conformal class produces a Killing ve...

The present paper deals with some results of submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-webster connection.

Recently Hui et al. (\cite{HAP}, \cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not exists any proper warped product...

The object of the present paper is to study the pseudoparallel, Ricci generalized pseudoparallel and η-parallel invariant submanifolds of (LCS)n-manifolds and we obtained some equivalent conditions of invariant submanifolds of (LCS)n-manifolds under which the submanifolds are totally geodesic. Among others we found the necessary and sufficient cond...

The object of the present paper is to study 3-dimensional β- Kenmotsu manifolds whose metric is Ricci soliton with respect to Schouten- van Kampen connection. We found the condition for the Ricci soliton structure to be invariant under Schouten-van Kampen connection. We have also showed that the Ricci soliton structure with respect to usual Levi-Ci...

A Kenmotsu manifold Mn(ϕ,ξ, η, g), (n = 2m+1 > 3) is called a generalized ϕ-recurrent if its curvature tensor R satisfies ϕ²((ΔWR)(X, Y)Z) = A(W)R(X, Y)Z + B(W)G(X; Y)Z for all X, Y, Z, W ∈ χ(M), where Δ denotes the operator of covariant differentiation with respect to the metric g, i.e. Δ is the Riemannian connection, A, B are non-vanishing 1-form...

The present paper deals with the study of Deszcz-pseudo parallel and Chaki-pseudo parallel contact CR-submanifolds of Ken-motsu manifolds with respect to Levi-Civita connection as well as semisymmetric metric connection and prove that corresponding these two classes are equivalent with a certain condition.

The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi-Civita connection and semisymmetric metric connection and obtain that these two classes are equivalent with a certain condition. Also the invariant and anti-invariant submanifolds of SQ-Sasa...

The present paper deals with the study of totally real submanifolds and $\textit{C}$-totally real submanifolds of $(LCS)_n$-manifolds with respect to Levi-Civita connection as well as quarter symmetric metric connection. It is proved that scalar curvature of $\textit{C}$-totally real submanifolds of $(LCS)_n$-manifold with respect to both the said...

The object of the present paper is to study Ricci solitons on Kenmotsu manifolds with respect to quarter symmetric non-metric φ-connection and obtain a necessary and sufficient condition of a Ricci soliton on a Kenmotsu manifold with respect to quarter symmetric non-metric φ-connection to be a Ricci soliton on a Kenmotsu manifold with respect to Le...

The present paper deals with the study of Ricci solitons on invariant and anti-invariant submanifolds of $(LCS)_n$-manifolds with respect to Riemannian connection as well as quarter symmetric metric connection.

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and obtain many new results including, the necessary and sufficient conditions under which the submanifolds are totally...

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and obtain many new results including, the necessary and sufficient conditions under which the submanifolds are totally...

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_{3}$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric $(LCS)...

The present paper deals with the study of generalized $\phi$-recurrent generalized $(k,\mu)$-contact metric manifolds with the existence of such notion by a proper example.

The object of the present paper is to study invariant submanifolds of (LCS)n-manifolds with respect to quarter symmetric metric connection. It is shown that the mean curvature of an invariant submanifold of (LCS)n-manifold with respect to quarter symmetric metric connection and Levi-Civita connection are equal. An example is constructed to illustra...

The present paper deals with the study of pseudo parallel (in the sense of Chaki and in the sense of Deszcz) contact CR-submanifolds with respect to Levi-Civita connection as well as semisymmetric metric connection of Kenmotsu manifolds and prove that these corresponding two classes are equivalent with a certain condition.

Abstract: The object of the present paper is to study warped product pseudo-slant submanifolds of (LCS)n-manifolds. We study the existence or non-existence of such submanifolds. The existence is also ensured by an example.

The present paper deals with a study of doubly warped product contact CR-submanifolds of (LCS)n-manifolds and warped product contact CR-submanifolds of (LCS)n-manifolds. It is shown that there exists no doubly warped product contact CR-submanifolds of (LCS)n-manifolds. However, we obtain some results for the existence or non-existence of warped pro...

The object of the present paper is to study concircular Ricci pseudosymmetric β-Kenmotsu manifolds whose metric is Ricci almost soliton. We found the conditions when Ricci almost soliton on concircular Ricci pseudosymmetric β-Kenmotsu manifold to be shrinking, steady and expanding respectively. We also construct an example of concircular Ricci pseu...

The object of the present paper is to study Ricci solitons on Para-Sasakian manifolds. We also study Ricci solitons on Para-Sasakian manifolds admitting a quarter symmetric metric connection and obtain a necessary and sufficient condition of a Ricci soliton on Para-Sasakian manifold admitting a quarter symmetric metric connection to be Ricci solito...

The object of this present paper is to study generalized ϕ-recurrent generalized Sasakian-space-forms and its various geometric properties. Among the results established here, it is shown that a generalized ϕ-recurrent generalized Sasakian-space-form is an Einstein manifold. Further, we study generalized concircular ϕ-recurrent generalized Sasakian...

The object of the present paper is to study η-Ricci solitons on η-Einstein Kenmotsu manifolds. It is shown that if the characteristic vector field ξ is a recurrent torse forming η-Ricci soliton on an η-Einstein Kenmotsu manifold then ξ is (i) concurrent and (ii) Killing vector field.

The present paper deals with a study of contact CR-warped product submanifolds of generalized Sasakian-space-forms and contact CR-warped product semi-slant submanifolds of generalized Sasakian-space-forms. It is shown that there exists no proper contact CR-warped product submanifolds of generalized Sasakian-space-forms. However, we obtain some resu...

The present paper deals with the study of Riemannian mani-folds whose metric is Ricci almost soliton with a conformal Killing vector field. We also study Ricci almost solitons on Riemannian manifolds with respect to semi-symmetric metric connection and obtain a necessary and sufficient condition of a Ricci almost soliton on Riemannian manifold with...

The present paper deals with the study of Riemannian mani-folds whose metric is Ricci almost soliton with a conformal Killing vector field. We also study Ricci almost solitons on Riemannian manifolds with respect to semi- symmetric metric connection and obtain a necessary and suffcient condition of a Ricci almost soliton on Riemannian manifold with...

The present paper deals with the study of generalized Sasakian-space-forms whose metric is Ricci soliton with potential vector field is conformal killing and obtain the conditions of such type of Ricci solitons to be expanding, steady and shrinking respectively.

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (ϕ, ξ, η, g) is a principal curvature vector field.

The present paper deals with the study of Ricci solitons on submanifolds, specially invariant and anti-invariant submanifolds of Kenmotsu manifolds with respect to Riemannian connection, quarter symmetric metric connection and quarter symmetric non-metric ϕ-connection, respectively.

As a generalization of quasi-Einstein manifold, De and Ghosh introduced the notion of generalized quasi-Einstein manifold. The object of the present paper is to study Ricci pseudosymmetric generalized quasi-Einstein manifolds (briey, G(QE)n) in the framework of pseudo-Riemannian geometry. Specifically, we study the concircular Ricci pseudosymmetric...

The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study semiparallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds. Among others we study 3-dimensional invariant submanifolds of (LCS)n-manifolds. It is shown that every 3-dimensional invariant submanifold of a (LCS)n-manifold is totally ge...

In this paper we study C-Bochner pseudosymmetric generalized Sasakian-space-forms and such space-forms with C-Bochner curvature tensor $$B$$B satisfying the conditions $$B(\xi , X)\cdot S=0$$B(ξ,X)·S=0, $$B(\xi , X)\cdot R=0$$B(ξ,X)·R=0 and $$B(\xi , X)\cdot B = 0$$B(ξ,X)·B=0, where $$R$$R and $$S$$S denotes the Riemann curvature tensor and Ricci t...

The object of the present paper is to study the second order parallel symmetric tensors and Ricci solitons on (LCS)n-manifolds. We found the conditions of Ricci soliton on (LCS)n-manifolds to be shrinking , steady and expanding respectively.

The object of the present paper is to study locally $\phi$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $\phi$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $\phi$-symmetric LP-Sasakian manifold with respect to...

The object of the present paper is to introduce the notion of weakly ∅-Ricci symmetric Kenmotsu manifolds and study characteristic properties of locally ∅-Ricci symmetric and ∅-recurrent spaces.

The present paper deals with a study of 3-dimensional contact metric generalized -space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized -space form with to be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric and -projectively flat, respectively.

The object of the present paper is to show that Theorem 3 of the paper [22] on 3-dimensional quasi-Sasakianmanifolds can be extended to 3-dimensional trans-Sasakian manifolds. We also find the curvature and torsion of Legendre curves in 3-dimensional trans-Sasakian manifolds with respect to semisymmetric metric connection. Keywords and phrases: Leg...

The present paper deals with a study of -pseudo symmetric and -pseudo Ricci symmetric -manifolds. It is shown that every -pseudo symmetric -manifold and -pseudo Ricci symmetric -manifold are -Einstein manifold.

We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudoslant produ...

The object of the present paper is to study φ-pseudo symmetric and φ-pseudo Ricci symmetric Kenmotsu manifolds with respect to quarter-symmetric metric connection and obtain a necessary and sufficient condition of a φ-pseudo symmetric Kenmotsu manifold with respect to quarter symmetric metric connection to be φ-pseudo symmetric Kenmotsu manifold wi...

The object of the present paper is to study the totally umbilical hypersurfaces of weakly projective symmetric spaces and it is shown that the totally umbilical hypersurfaces of a weakly projective symmetric space are also weakly projective symmetric spaces.

In this paper, we present the sectional curvature of nearly quasi-Einstein manifolds whose associated tensor E of type (0, 2) is given by E(X, Y) = A(X)B(Y) + A(Y)B(X).

The object of the present paper is to study φ-pseudo symmetric and φ-pseudo Ricci symmetric Kenmotsu manifolds. We also studied φ-pseudo concircularly symmetric Kenmotsu manifolds and obtained a number of results.

The object of the present paper is to study an N(k)-quasi Einstein manifold admitting W2-curvature tensor. Also, we study generalized Ricci recurrent N(k)-quasi Einstein manifolds.

We study of warped product submanifolds, especially warped product hemi-slant submanifolds of LP-Sasakian manifolds. We obtain the results on the nonexistance or existence of warped product hemi-slant submanifolds and give some examples of LP-Sasakian manifolds. The existence of warped product hemi-slant submanifolds of an LP-Sasakian manifold is a...

This paper deals with the study of super quasi-Einstein manifolds admitting 𝑊2-curvature tensor. The totally umbilical hypersurfaces of 𝑆(𝑄𝐸)𝑛 are also studied. Among others, the existence of such a manifold is ensured by a nontrivial example.

The object of the present paper is to study weakly ϕ-symmetric and weakly ϕ-Ricci symmetric Kenmotsu manifolds. It is shown that weakly ϕ-symmetric and weakly ϕ-Ricci symmetric Kenmotsu manifolds are η-Einstein.

A new curvature tensor, called W2-curvature tensor, was defined by G. P. Pokhariyal and R. S. Mishra in [Yokohama Math. J. 18, 105–108 (1970; Zbl 0228.53022)]. In this paper, we study generalized quasi Einstein manifolds admitting a W2-curvature tensor. The existence of such manifolds is ensured by some interesting examples.

The object of the present paper is to study almost pseudo concircular Ricci symmetric manifolds and its decomposibility. Among others it is shown that in a decomposable almost pseudo concircular Ricci symmetric manifold one of the decompositions is Einstein and the other decomposition is concircular Ricci symmetric. The totally umbilical hypersurfa...

The object of the present paper is to study weakly concircular symmetric and weakly concircular Ricci symmetric trans-Sasakian manifolds.

The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study Lorentzian quasi-Einstein manifolds. Some basic ge...

The object of the present paper is to study concircularly symmetric (PCRS)n, concircularly recurrent (PCRS)n, decomposable (PCRS)n. Among others it is shown that in a decomposable (PCRS)n one of the decompositions is Ricci flat and the other decomposition is cyclic parallel. The totally umbilical hypersurfaces of (PCRS)n are also studied. Key word...

The object of the present paper is to study concircularly symmetric (PCRS)n, con circularly recurrent (PCRS)n, decomposable (PCRS)n. Among others it is shown that in a decomposable (PCRS)n one of the decompositions is Ricci flat and the other decomposition is cyclic parallel. The totally umbilical hypersurfaces of (PCRS)n are also studied.

The present paper deals with a study of some global prop-erties of pseudo cyclic Ricci symmetric manifolds. It is shown that in a compact, orientable pseudo cyclic Ricci symmetric manifold without boundary, there exists no non-zero Killing (resp., projective Killing, con-formal Killing) vector field, and also it is proved that in such a manifold a...

We extend the notion of generalized φ-recurrent β-Kenmotsu man-ifold and study its various geometric properties with the existence of such notion.

We study some classes of generalized ϕ-recurrent Saskian manifolds such as generalized projectively ϕ-recurrent Saskian manifolds and generalized conharmonically ϕ-recurrent Saskian manifolds.