Showing papers by "Uday Chand De published in 2019"

Yamabe Solitons and Ricci Solitons on Almost co-Kähler Manifolds

Abstract: The object of this paper is to study Yamabe solitons on almost co-Kahler manifolds as well as on -almost co-Kahler manifolds.

Perfect fluid spacetimes with harmonic generalized curvature tensor

Abstract: We show that $n$-dimensional perfect fluid spacetimes with diver\-gen\-ce-free conformal curvature tensor and constant scalar curvature are generalized Robertson Walker (GRW) spacetimes; as a consequence a perfect fluid Yang pure space is a GRW spacetime. We also prove that perfect fluid spacetimes with harmonic generalized curvature tensor are, under certain conditions, GRW spacetimes. As particular cases, perfect fluids with divergence-free projective, concircular, conharmonic or quasi-conformal curvature tensor are GRW spacetimes. Finally, we explore some physical consequences of such results.

*-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.

Sequential warped products: curvature and conformal vector fields

Abstract: 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 field 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 space-times and sequential standard static space-times.

Generalized quasi-Einstein GRW space-times

Abstract: Recently, it is proven that generalized Robertson–Walker space-times in all orthogonal subspaces of Gray’s decomposition except one (unrestricted) are perfect fluid space-times. GRW space-times in ...

Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection

Abstract: We define a new type of quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold and prove its existence. We provide its application in the general theory of relativity. To validate the existence of the quarter-symmetric non-metric $\xi$-connection on an $LP$-Sasakian manifold, we give a non-trivial example in dimension $4$ and verify our results.

$$\eta $$ η -Ricci solitons in $$\epsilon $$ ϵ -Kenmotsu manifolds

Abstract: The object of the present paper is to characterize $$\epsilon $$ -Kenmotsu manifolds admitting $$\eta $$ -Ricci solitons Finally, the existence of $$\eta $$ -Ricci soliton in an $$\epsilon $$ -Kenmotsu manifold has been proved by a concrete example

Some characterizations of Lorentzian manifolds

Abstract: Generalized Robertson–Walker (GRW) spacetime is the generalization of the Robertson–Walker (RW) spacetime and a further generalization of GRW spacetime is the twisted spacetime. In this paper, we g...

Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions

Abstract: The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (k; μ)-, (k; μ)′-, and generalized (k; μ)-nullity distributions. We also characterize (k; μ)-almost Kenmotsu manifolds satisfying the condition R ⋅ S = LꜱQ(g; S2).

Concircular curvature on warped product manifolds and applications.

Abstract: 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.

Golden Riemannian structures on the tangent bundle with g-natural metrics

Abstract: Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

On Pseudo Q-symmetric spacetimes

Abstract: In this paper, we investigate pseudo Q-symmetric spacetimes $$(PQS)_{4}$$ . At first, we prove that a $$(PQS)_{4}$$ spacetime is a quasi-Einstein spacetime. Then we investigate perfect fluid $$(PQS)_{4}$$ spacetimes and interesting properties are pointed out. From a result of Mantica and Suh (Int J Geom Methods Mod Phys 10:1350013, 2013) we have shown that $$(PQS)_{4}$$ spacetime is the Robertson-Walker spacetime. Further, it is shown that a $$(PQS)_{4}$$ spacetime with cyclic parallel Ricci tensor is an Einstein spacetime. Finally, we construct an example of a $$(PQS)_{4}$$ spacetime.

On generalized quasi-Einstein GRW space-times

Abstract: 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.

On weakly semiconformally symmetric manifolds

Abstract: The object of the present paper is to study weakly semiconformally symmetric manifolds (WSCS)n. At first some geometric properties of (WSCS)n (n > 2) have been studied. Finally, we consider the decomposability of (WSCS)n.

On Interpolating Sesqui-Harmonic Legendre Curves in Sasakian Space Forms

Abstract: 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.

Classifications of $K$-Contact Semi-Riemannian Manifolds

Abstract: The object of the present paper is to characterize a K-contact semi-Riemannian manifold satisfying certain curvature conditions. We study Ricci semi-symmetric K-contact semi-Riemannian manifolds and obtain an equivalent condition. Next we prove that a K-contact semi-Riemannian manifold is of harmonic conformal curvature tensor if and only if the manifold is an Einstein manifold. Also we study $\xi$-conformally flat K-contact semi-Riemannian manifolds. Finally, we charecterize conformally semisymmetric Lorentzian $K$-contact manifolds.