Integral formulas in Riemannian geometry

On conharmonic transformations of weyl spaces

In this paper, we study para-Sasakian manifold (M,g) whose metric g is an η-Ricci soliton (g,V ) and almost η-Ricci soliton. We prove that, if g is an η-Ricci soliton, then either M is Einstein and...

η-Ricci solitons and almost η-Ricci solitons on para-Sasakian manifolds

In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field $$\xi $$
 are described 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.

Ricci soliton and geometrical structure in a perfect fluid spacetime with torse-forming vector field

In this paper we study a special type of metric called $$*$$
 -Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a $$*$$
 -Ricci soliton on a manifold M, then M is either $$\mathcal {D}$$
 -homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.

Para-Sasakian manifolds and $$*$$ ∗ -Ricci solitons

Abstract In this paper, we consider *-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if (M, g) is a Kenmotsu manifold and g is a *-Ricci soliton, then soliton constant λ is zero. For 3-dimensional case, if M admits a *-Ricci soliton, then we show that M is of constant sectional curvature –1. Next, we show that if M admits a *-Ricci soliton whose potential vector field is collinear with the characteristic vector field ξ, then M is Einstein and soliton vector field is equal to ξ. Finally, we prove that if g is a gradient almost *-Ricci soliton, then either M is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of M. We verify our result by constructing examples for both *-Ricci soliton and gradient almost *-Ricci soliton.

∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

The purpose of this paper is to study 3-dimensional paraSasakian manifold and conformally flat K-paracontact manifold. Moreover, we show that in a K-paracontact manifold the conditions Einstein, conformally flat, semi-symmetric and Ricci semi-symmetric are all equivalent. Finally, compact regular 3-dimensional paraSasakian and conformally flat K-paracontact manifolds are studied.

Certain results on K-paracontact and paraSasakian 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 $-\varepsilon$.

/pdf/certain-results-on-kenmotsu-pseudo-metric-manifolds-20xrlu40yo.pdf

Certain results on Kenmotsu pseudo-metric manifolds

The purpose of this paper is to study the Fischer–Marsden conjecture on a class of almost Kenmotsu manifolds. We characterize non-Kenmotsu $$(\kappa , \mu )^\prime $$
 -almost Kenmotsu manifolds satisfying the Fischer–Marsden equation.

The Fischer–Marsden conjecture on non-Kenmotsu $$(\kappa , \mu )^\prime $$ ( κ , μ ) ′ -almost Kenmotsu manifolds

The present paper deals with the study of generalized B curvature tensor on (LCS)n-manifolds. Here we describe flatness, semisymmetry and recurrent properties on (LCS)n-manifolds. Moreover we consider the conditions B ·R = 0, B ·B = 0 and B ·S = 0 and obtained interesting results

Venkatesha

Papers

∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds

Certain results on K-paracontact and paraSasakian manifolds

Certain results on Kenmotsu pseudo-metric manifolds

The Fischer–Marsden conjecture on non-Kenmotsu $$(\kappa , \mu )^\prime $$ ( κ , μ ) ′ -almost Kenmotsu manifolds

The generalized $B$ curvature tensor on $(LCS)_{n}$-manifolds