arXiv research

The paper examines Ricci solitons on specific types of $(LCS)_n$-manifolds.

The paper classifies a specific type of contact metric manifolds.

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 paper investigates various generalizations of semisymmetric and pseudosymmetric manifolds.

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 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 paper examines curvature properties of a specific magnetic spacetime metric.

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

The paper examines curvature properties of Vaidya metric, a generalization of Schwarzschild solution.

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…

The paper examines curvature properties of charged Nariai spacetimes.

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

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

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…

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 examines geometric properties of a specific black hole spacetime.

The study characterizes symmetries in Kaehler manifolds.

Geodesic mappings found in a specific type of warped product manifolds.

Investigates geometric properties of Bardeen black hole spacetime.

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

The paper classifies certain $N(κ)$-contact metric manifolds under specific conditions.

Study properties of hyperbolic Yamabe solitons in submanifolds.

The paper studies $(ε)$-para-Sasakian 3-manifolds with $\mathcal{Z}$-symmetry conditions.

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

The paper examines conditions for Ricci solitons to be Ricci flat or Einstein.

Study stability and instability of Ricci-flat metrics under generalized Ricci flow.

Study ancient Ricci flows with nonnegative Ricci curvature and their asymptotic geometry.

Study of $η$-Ricci solitons on Kenmotsu 3-manifolds.

Survey paper analyzes curvature estimates for 4D gradient Ricci solitons.

Defines projective Ricci curvature and proves rigidity for sprays.

Paper introduces $*-$Ricci flow and its properties.

The paper examines Ricci solitons with convex potential and finds them flat and split.

ALE Ricci-flat manifolds stable under Ricci flow if integrable.

Study on transverse Ricci solitons on compact foliated manifolds.

The paper examines how parabolic frequency behaves under Ricci flow and Ricci-harmonic flow on manifolds.

The paper explores almost Ricci solitons on Finsler spaces, proving conditions for their existence.

Existence of Kähler-Ricci soliton on smooth Fano horospherical manifolds proven.

New graphs with maximum degree 4 found to be Ricci-flat.

The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.

Study on Ricci-Bourguignon solitons and almost solitons, generalizing previous results.

Study characterizes Einstein manifolds in almost Ricci solitons.

In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or steady) gradient Kähler-Ricci solitons with positively pinched Ricci curvature sho…

Equivalence proven between different Ricci curvature definitions.

Study heat kernel on Ricci shrinkers with sharper estimates.

Surveying Ricci flow and its applications to Ricci limit spaces.