Devaraja Mallesha Naik

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.

Some results on almost Kenmotsu manifolds

Abstract: First we consider almost Kenmotsu manifolds which satisfy Codazzi condition for and , and we prove that in such cases the tensor vanishes. Next, we prove that an almost Kenmotsu manifold having constant -sectional curvature which is locally symmetric is a Kenmotsu manifold of constant curvature . We also prove that, for a -almost Kenmotsu manifold of with , every conformal vector field is Killing. Finally, we prove that if is a -almost Kenmotsu manifold with and , then the vector field which leaves the curvature tensor invariant is Killing.

Riemann solitons and almost Riemann solitons on 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.

Characterization of Ricci Almost Soliton on Lorentzian Manifolds

Abstract: Ricci solitons (RS) have an extensive background in modern physics and are extensively used in cosmology and general relativity. The focus of this work is to investigate Ricci almost solitons (RAS) on Lorentzian manifolds with a special metric connection called a semi-symmetric metric u-connection (SSM-connection). First, we show that any quasi-Einstein Lorentzian manifold having a SSM-connection, whose metric is RS, is Einstein manifold. A similar conclusion also holds for a Lorentzian manifold with SSM-connection admitting RS whose soliton vector Z is parallel to the vector u. Finally, we examine the gradient Ricci almost soliton (GRAS) on Lorentzian manifold admitting SSM-connection.

Generalized Ricci soliton and paracontact geometry

Abstract: In the present paper, we study generalized Ricci soliton in the framework of paracontact metric manifolds. First, we prove that if the metric of a paracontact metric manifold M with $$Q\varphi =\varphi Q$$ is a generalized Ricci soliton (g, X) and if $$X e 0$$ is pointwise collinear to $$\xi$$ , then M is K-paracontact and $$\eta$$ -Einstein. Next, we consider closed generalized Ricci soliton on K-paracontact manifold and prove that it is Einstein provided $$\beta (\lambda +2n\alpha ) e 1$$ . Next, we study K-paracontact metric as gradient generalized almost Ricci soliton and in this case we prove that (i) the scalar curvature r is constant and is equal to $$-2n(2n+1)$$ ; (ii) the squared norm of Ricci operator is constant and is equal to $$4n^2(2n+1)$$ , provided $$\alpha \beta e -1$$ .

η-Ricci solitons and almost η-Ricci solitons on para-Sasakian manifolds

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...

*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds

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.

Ricci soliton and geometrical structure in a perfect fluid spacetime with torse-forming vector field

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.

Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

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.