arXiv research

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, conforma…

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for ${\cal T}_{a}$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained. $({\cal T}_{a},{\cal T}_{b…

In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […

The curvature properties of Robinson-Trautman metric have been investigated. It is shown that Robinson-Trautman metric admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Also it is shown that the difference $R…

The object of the present paper is to study the characterization of warped product manifolds satisfying some pseudosymmetric type conditions, especially, due to projective curvature tensor. For this purpose we consider a warped product manifold satisfying the pseudosymmetric type condition $R\cdot R = L_1 Q(g,R) + L_2 …

The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.

This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in gen…

In this paper we classify Ricci-generalized pseudosymmetric $(κ, μ)$-contact metric manifolds in the sense of Deszcz .

The aim of this paper is to present examples of Kahler holomorphically pseudosymmetric metrics on the projective space CP^n.

For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct exampl…

The study characterizes symmetries in Kaehler manifolds.

The paper investigates various generalizations of semisymmetric and pseudosymmetric manifolds.

Investigates geometric properties of Bardeen black hole spacetime.

The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a $2$-dimentional de-Sitter spacetime with a round $2$-sphere of constant radius. The present paper deals with the investigation of curv…

The projective curvature tensor $P$ is invariant under a geodesic preserving transformation on a semi-Riemannian manifold. It is well known that $P$ is not a generalized curvature tensor and hence it possesses different geometric properties than other generalized curvature tensors. The main object of the present paper …

Study properties of hyperbolic Yamabe solitons in submanifolds.

We determine a particular class of Roter type warped product manifolds. We show that every manifold of that class admits a geodesic mapping onto a some Roter type warped product manifold. Moreover, both geodesically related manifolds are pseudosymmetric of constant type.

The object of this paper is study $(ε)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and projectively $\mathcal{Z}$-semisymmetric conditions on an $(ε)$-para-Sasakian 3-manifold.

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spaceti…

The paper explores symmetries in Kähler manifolds using Ricci tensor properties.

The paper examines geometric properties of a specific black hole spacetime.

In this paper, $N(κ)$-contact metric manifolds satisfying the conditions $\widetilde{C}(ξ,X)\cdot\widetilde{C}=0$, $\widetilde{C}(ξ,X)\cdot R=0$, $\widetilde{C}(ξ,X)\cdot S=0$, $\widetilde{C}(ξ,X)\cdot C=0$, $C\cdot S=0$ and $R\cdot C=f_{C}Q(g,C)$ have been investigated and obtained their classification. Among others i…

In this paper we study the 3-dimensional $(\varepsilon)$-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon )$-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric $(\varepsilon)$-para Sasakian 3 -manifold is an indefinite space form…

As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties of Vaidya metric. It is shown that Vaidya metric can be cons…

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

Study geometric properties and physical applications of mixed quasi-Einstein spacetime.