Author

# Venkatesha Venkatesh

Bio: Venkatesha Venkatesh is an academic researcher. The author has contributed to research in topics: Soliton & Vector field. The author has an hindex of 1, co-authored 1 publications receiving 10 citations.

Topics: Soliton, Vector field

##### Papers

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TL;DR: In this paper, the authors consider the case where the potential vector field is collinear with the characteristic vector field on an open set of manifolds and show that the potential field is equal to the soliton vector field.

Abstract: In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold $M$ is a $*$-Ricci soliton, then soliton constant $\lambda$ 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 $\xi$, then $M$ is Einstein and soliton vector field is equal to $\xi$. 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.

10 citations

##### Cited by

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TL;DR: In this paper, the authors studied the Riemann soliton and gradient almost-Riemann-soliton on a certain class of almost Kenmotsu manifolds.

Abstract: The aim of this paper, is to study the Riemann soliton and gradient almost Riemann soliton on certain class of almost Kenmotsu manifolds. Also, some suitable examples of Kenmotsu and (κ,μ)′-almost ...

5 citations

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15 Apr 2021

TL;DR: In this article, it was shown that Bach flat almost coKahler manifold admits Ricci solitons, satisfying the critical point equation (CPE) or Bach flat.

Abstract: In this paper, we study an almost coKahler manifold admitting certain metrics such as $$*$$
-Ricci solitons, satisfying the critical point equation (CPE) or Bach flat. First, we consider a coKahler 3-manifold (M, g) admitting a $$*$$
-Ricci soliton (g, X) and we show in this case that either M is locally flat or X is an infinitesimal contact transformation. Next, we study non-coKahler $$(\kappa ,\mu )$$
-almost coKahler metrics as CPE metrics and prove that such a g cannot be a solution of CPE with non-trivial function f. Finally, we prove that a $$(\kappa , \mu )$$
-almost coKahler manifold (M, g) is coKahler if either M admits a divergence free Cotton tensor or the metric g is Bach flat. In contrast to this, we show by a suitable example that there are Bach flat almost coKahler manifolds which are non-coKahler.

3 citations

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TL;DR: In this article, it was shown that if the metric g represents a Yamabe soliton, then it is locally isometric to the product space and the contact transformation is a strict infinitesimal contact transformation.

Abstract: Let $$(M^{2n+1},\phi ,\xi ,\eta ,g)$$
be a non-Kenmotsu almost Kenmotsu $$(k,\mu )'$$
-manifold. If the metric g represents a Yamabe soliton, then either $$M^{2n+1}$$
is locally isometric to the product space $$\mathbb {H}^{n+1}(-4)\times \mathbb {R}^n$$
or $$\eta $$
is a strict infinitesimal contact transformation. The later case can not occur if a Yamabe soliton is replaced by a gradient Yamabe soliton. Some corollaries of this theorem are given and an example illustrating this theorem is constructed.

2 citations

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TL;DR: In this paper, the authors studied the Riemann soliton and gradient almost-Riemann-soliton on a class of almost-Kenmotsu manifolds.

Abstract: The aim of this article is to study the Riemann soliton and gradient almost Riemann soliton on certain class of almost Kenmotsu manifolds. Also some suitable examples of Kenmotsu and $(\kappa,\mu)'$-almost Kenmotsu manifolds are constructed to justify our results.

2 citations