Author
Devaraja Mallesha Naik
Other affiliations: Christ University
Bio: Devaraja Mallesha Naik is an academic researcher from Kuvempu University. The author has contributed to research in topics: Soliton & Vector field. The author has an hindex of 7, co-authored 22 publications receiving 104 citations. Previous affiliations of Devaraja Mallesha Naik include Christ University.
Papers
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TL;DR: In this paper, the authors considered the case of *-Ricci soliton in the framework of a Kenmotsu manifold and proved that soliton constant λ is zero.
Abstract: 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.
29 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...
28 citations
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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...
17 citations
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TL;DR: In this paper, a 3-dimensional paraSasakian manifold and a conformally flat K-paracontact manifold were studied and it was shown that the conditions Einstein, conformal flat, semi-symmetric, and Ricci semi symmetric are all equivalent.
Abstract: 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.
14 citations
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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
Cited by
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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
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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.
24 citations
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01 Sep 2019
TL;DR: In this paper, geometrical aspects of perfect fluid spacetime with torse-forming vector field are described and conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
Abstract: 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.
21 citations
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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