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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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Journal ArticleDOI
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 $-\varepsilon$.

10 citations

Journal ArticleDOI
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 ...

10 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this article, it was shown that a Riemannian manifold equipped with a concurrent-recurrent vector field is of constant negative curvature when its metric is a Ricci soliton.
Abstract: In this paper, we initiate the study of impact of the existence of a unit vector $$ u $$ , called a concurrent-recurrent vector field, on the geometry of a Riemannian manifold. Some examples of these vector fields are provided on Riemannian manifolds, and basic geometric properties of these vector fields are derived. Next, we characterize Ricci solitons on 3-dimensional Riemannian manifolds and gradient Ricci almost solitons on a Riemannian manifold (of dimension n) admitting a concurrent-recurrent vector field. In particular, it is proved that the Riemannian 3-manifold equipped with a concurrent-recurrent vector field is of constant negative curvature $$-\alpha ^2$$ when its metric is a Ricci soliton. Further, it has been shown that a Riemannian manifold admitting a concurrent-recurrent vector field, whose metric is a gradient Ricci almost soliton, is Einstein.

8 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
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

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