Certain results on (LCS)n-manifolds
The purpose of the present paper is to study semi-generalized recurrent, semi-generalized Ricci recurrent and conformal Ricci soliton on (LCS)n-manifold.
math.DG↗
arXiv subjects
Venkatesha
Publications and source records attributed to Venkatesha.
Results on para-Sasakian manifold admitting a quarter symmetric metric connection
In this paper we have studied pseudosymmetric, Ricci-pseudosymmetric and projectively pseudosymmetric para-Sasakian manifold admitting a quarter-symmetric metric connection and constructed examples of 3-dimensional and 5-dimensional para-Sasakian manifold admitting a quarter-symmetric metric connection to verify our results.
math.GM↗
Certain Curvature Conditions on N(k)-Paracontact Metric Manifolds
The aim of the present paper is to study pseudo-symmetric, Ricci generalized pseudo-symmetric and generalized Ricci recurrent N(k)-Paracontact Metric Manifolds.
math.GM↗
Certain results on Kenmotsu pseudo-metric manifolds
In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.
math.DG↗
Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field \xi are discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field \xi are determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
math.DG↗
Certain results on almost contact pseudo-metric manifolds
We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields $h:=\frac{1}{2}\pounds _\xi \varphi$ and $\ell := R(\cdot,\xi)\xi$, emphasizing analogies and differences with respect to the contact metric case. Certain identities involving $\xi$-sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost $CR$ structure $(\mathcal{H}(M), J, \theta)$ corresponding to almost contact pseudo-metric manifold $M$ to be $CR$ manifold. Finally, we prove that a contact pseudo-metric manifold $(M,\varphi,\xi,\eta,g)$ is Sasakian if and only if the corresponding nondegenerate almost $CR$ structure $(\mathcal{H}(M), J)$ is integrable and $J$ is parallel along $\xi$ with respect to the Bott partial connection.
math.DG↗