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V. Venkatesha

Bio: V. Venkatesha is an academic researcher from Kuvempu University. The author has contributed to research in topics: Physics & Manifold (fluid mechanics). The author has an hindex of 6, co-authored 27 publications receiving 97 citations.

Papers
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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...

28 citations

Journal ArticleDOI
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.

17 citations

Journal ArticleDOI
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...

17 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation admits a gradient, then either the potential function is pointwise collinear with the Reeb vector field or the gradient is Einstein.
Abstract: In this paper, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation admits a gradient $$\rho $$ -Einstein soliton, then either $$M^{2n+1}$$ is Einstein or the potential function is pointwise collinear with the Reeb vector field $$\xi $$ on an open set $${\mathcal {O}}$$ of $$M^{2n+1}$$ . Moreover, we prove that if the metric of a $$(\kappa ,-2)'$$ -almost Kenmotsu manifold with $$h' e 0$$ admits a gradient $$\rho $$ -Einstein soliton, then the manifold is locally isometric to the Riemannian product $${\mathbb {H}}^{n+1}(-4)\times {\mathbb {R}}^n$$ and potential vector field is tangential to the Euclidean factor $${\mathbb {R}}^n$$ . We show that there does not exist gradient $$\rho $$ -Einstein soliton on generalized $$(\kappa ,\mu )$$ -almost Kenmotsu manifold of constant scalar curvature. Finally, we construct an example for gradient $$\rho $$ -Einstein soliton.

15 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of paracontact geometry on a para-Kenmotsu manifold and showed that if the metric g of g of G of σ, σ is a Gaussian, then G is either the potential vector field collinear with Reeb vector field or Ricci soliton.
Abstract: We consider almost $$*$$ -Ricci solitons in the context of paracontact geometry, precisely, on a paraKenmotsu manifold. First, we prove that if the metric g of $$\eta $$ -Einstein paraKenmotsu manifold is $$*$$ Ricci soliton, then M is Einstein. Next, we show that if $$\eta $$ -Einstein paraKenmotsu manifold admits a gradient almost $$*$$ -Ricci soliton, then either M is Einstein or the potential vector field collinear with Reeb vector field $$\xi $$ . Finally, for three-dimensional case we show that paraKenmotsu manifold is of constant curvature $$-1$$ . An illustrative example is given to support the obtained results.

12 citations


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Book
01 Jan 1970

329 citations

Journal ArticleDOI
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...

28 citations

Journal ArticleDOI
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.

24 citations

Journal ArticleDOI
TL;DR: In this paper , it was shown that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein.
Abstract: Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

20 citations