Author

# V. Venkatesha

Bio: V. Venkatesha is an academic researcher from Kuvempu University. The author has contributed to research in topic(s): Manifold & Riemann curvature tensor. The author has an hindex of 6, co-authored 27 publication(s) receiving 97 citation(s).

##### Papers

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TL;DR: In this paper, a 3D contact metric manifold such that Qφ = φQ which admits a Yamabe soliton (g,V ) with the flow vector field V pointwise collinear with the Reeb vector field ξ is considered.

Abstract: If M is a 3-dimensional contact metric manifold such that Qφ = φQ which admits a Yamabe soliton (g,V ) with the flow vector field V pointwise collinear with the Reeb vector field ξ, then we show th...

13 citations

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TL;DR: In this paper, the authors studied a para-Sakian manifold whose metric g is an η-Ricci soliton (g,V ) and almost η Ricci solitons.

Abstract: 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...

11 citations

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TL;DR: In this paper, a contact metric manifold whose metric is a Riemann soliton was studied and it was shown that the manifold is either of constant curvature + 1 (and V is Killing) or D-homothetically invariant.

Abstract: In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g; V ) with V as contact vector eld on a Sasakian manifold (M; g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically xed -Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K-contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S2n+1. Further, we study H-contact manifold admitting a Riemann soliton (g; V ) where V is pointwise collinear with .Key words: Contact metric manifold, Riemann soliton, gradient almost Riemann soliton.

11 citations

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7 citations

27 Oct 2017

TL;DR: In this article, the authors studied M -projectively flat generalized Sasakian space form, η-Einstein generalized space form and irrotational M-projective curvature tensor tensor on a SSA.

Abstract: In the present paper, we have studied M -projectively flat generalized Sasakian space form, η-Einstein generalized Sasakian space form and irrotational M -projective curvature tensor on a Sasakian space form.

6 citations

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471 citations

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TL;DR: In this article, it was shown that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation.

Abstract: Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.

12 citations

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TL;DR: In this paper, the authors studied a para-Sakian manifold whose metric g is an η-Ricci soliton (g,V ) and almost η Ricci solitons.

Abstract: 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...

11 citations

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TL;DR: In this article, a systematic study of Kenmotsu pseudo-metric manifolds is presented, and the Ricci solitons on these manifolds are considered, and necessary and sufficient conditions for them to have constant curvatures are provided.

Abstract: 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 $-\varepsilon$.

8 citations