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Uday Chand De

Publications and source records attributed to Uday Chand De.

28 records · Page 2Linked to original sources
arXiv2021

H-almost Ricci-Yamabe solitons in paracontact geometry

In this article, we classify h-almost Ricci-Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci-Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci-Yamabe solitons. Next, we classify para-Sasakian manifolds admitting h-almost Ricci-Yamabe solitons and h-almost gradient Ricci-Yamabe solitons. Besides these, we investigate h-almost Ricci-Yamabe solitons and h-almost gradient Ricci-Yamabe solitons in para-cosymplectic manifolds. Finally, we construct two examples to illustrate our results.

math.DG↗
arXiv2021

A complete study of conformally flat pseudo-symmetric spacetimes in the theory of F(R)-gravity

We investigate the geometrical and physical structures of a pseudo-symmetric spacetime $(PS)_4$ with timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed velocity vector. We further study this spacetime as a solution of $F(R)$-gravity theory and show that the pressure and energy density of the effective cosmological perfect fluid separately possess certain typical relations with the geometry and the gravity sector of the theory. Based on this result, some observational and cosmological analyses are done for the $F(R)$-gravity model and the energy conditions are investigated, supporting the accelerated expansion of the universe.

gr-qc↗
arXiv2021

Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime

The aim of the present paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson-Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson-Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein's field equations without cosmological constant is vacuum. Finally, we construct a non-trivial example of pseudosymmetric spacetime.

gr-qc↗
arXiv2020

A note on Almost Riemann Soliton and gradient almost Riemann soliton

The quest of the offering article is to investigate \emph{almost Riemann soliton} and \emph{gradient almost Riemann soliton} in a non-cosymplectic normal almost contact metric manifold $M^3$. Before all else, it is proved that if the metric of $M^3$ is Riemann soliton with divergence-free potential vector field $Z$, then the manifold is quasi-Sasakian and is of constant sectional curvature -$λ$, provided $α,β=$ constant. Other than this, it is shown that if the metric of $M^3$ is \emph{ARS} and $Z$ is pointwise collinear with $ξ$ and has constant divergence, then $Z$ is a constant multiple of $ξ$ and the \emph{ARS} reduces to a Riemann soliton, provided $α,\;β=$constant. Additionally, it is established that if $M^3$ with $α,\; β=$ constant admits a gradient \emph{ARS} $(γ,ξ,λ)$, then the manifold is either quasi-Sasakian or is of constant sectional curvature $-(α^2-β^2)$. At long last, we develop an example of $M^3$ conceding a Riemann soliton.

math.DG↗
arXiv2019

Concircular curvature on warped product manifolds and applications

This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson-Walker and standard static space-times.

math.DG↗
arXiv2019

Sequential Warped Products: Curvature and Killing Vector Fields

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker spacetimes and sequential standard static spacetimes.

math.DG↗
arXiv2019

On generalized quasi-Einstein GRW space-times

Recently, it is proven that generalized Robertson-Walker space-times in all orthogonal subspaces of Gray's decomposition but one(unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a constant scalar curvature. It is shown that generalized quasi-Einstein GRW space-times reduce to Einstein space-times or perfect fluid space-times.

math.DG↗
arXiv2019

On Interpolating Sesqui-Harmonic Legendre Curves in Sasakian Space Forms

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.

math.DG↗
arXiv2016

A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time

A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity vector field is zero. Conversely, a generalized Robertson-Walker space-time with null divergence of the Weyl tensor is a perfect-fluid space-time.

math.DG↗