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.

Observational Insights into the Accelerating Universe through Reconstruction of the Deceleration Parameter

Abstract: Recent developments in the exploration of the universe suggest its accelerated phase of expansion. In this regard, our manuscript aims to probe the current scenario of the universe with the aid of the reconstruction technique. The primary factor that describes cosmic evolution is the deceleration parameter. Here, we provide a physically plausible, newly defined, model-independent parametric form of the deceleration parameter. Further, we constrain the free parameters through statistical MCMC analysis for different datasets, including the most recent Pantheon+. With the statistically obtained results, we analyze the dynamics of the model through the phase transition, EoS parameter and energy conditions. Also, we make use of the tool Om diagnostic to test our model.

Certain results on almost contact pseudo-metric manifolds

Abstract: We study the geometry of almost contact pseudo-metric manifolds in terms of tensor fields $h:=\frac{1}{2}\pounds _\xi \varphi$ and $\ell := R(\cdot,\xi)\xi$, emphasizing analogies and differences with respect to the contact metric case. Certain identities involving $\xi$-sectional curvatures are obtained. We establish necessary and sufficient condition for a nondegenerate almost $CR$ structure $(\mathcal{H}(M), J, \theta)$ corresponding to almost contact pseudo-metric manifold $M$ to be $CR$ manifold. Finally, we prove that a contact pseudo-metric manifold $(M,\varphi,\xi,\eta,g)$ is Sasakian if and only if the corresponding nondegenerate almost $CR$ structure $(\mathcal{H}(M), J)$ is integrable and $J$ is parallel along $\xi$ with respect to the Bott partial connection.

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.