Arindam Bhattacharyya

Bio: Arindam Bhattacharyya is an academic researcher from Jadavpur University. The author has contributed to research in topics: Sasakian manifold & Einstein manifold. The author has an hindex of 6, co-authored 69 publications receiving 209 citations.

$$*$$ ∗ - $$\eta $$ η -Ricci soliton and contact geometry

Abstract: In the present paper, we initiate the study of $$*$$ - $$\eta $$ -Ricci soliton within the framework of Kenmotsu manifolds as a characterization of Einstein metrics. Here we display that a Kenmotsu metric as a $$*$$ - $$\eta $$ -Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have developed the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost $$*$$ - $$\eta $$ -Ricci soliton. Next, we deliberate $$*$$ - $$\eta $$ -Ricci soliton admitting $$(\kappa ,\mu )^\prime $$ -almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to $${\mathbb {H}}^{n+1}(-4)\times {\mathbb {R}}^n$$ . Finally we present some examples to decorate the existence of $$*$$ - $$\eta $$ -Ricci soliton, gradient almost $$*$$ - $$\eta $$ -Ricci soliton on Kenmotsu manifold.

Contact CR-Submanifolds of an Indefinite Trans-Sasakian Manifold

Abstract: This paper is based on contact CR-submanifolds of an indefinite trans-Sasakian manifold of type (α, β). Here some properties of contact CR-submanifolds of an indefinite trans-Sasakian manifold have been studied and also the sectional curvatures of contact CR-submanifolds of an indefinite trans-Sasakian space form are discussed.

Some results on {\eta}-Yamabe Solitons in 3-dimensional trans-Sasakian manifold.

Abstract: The object of the present paper is to study some properties of 3-dimensional trans-Sasakian manifold whose metric is {\eta}-Yamabe soliton. We have studied here some certain curvature conditions of 3-dimensional trans-Sasakian manifold admitting {\eta}-Yamabe soliton. Lastly we construct a 3-dimensional trans-Sasakian manifold satisfying {\eta}-Yamabe soliton.

On Ricci flat warped products with a quarter-symmetric connection

Abstract: In this paper, we have computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of M [i.e; (1). dimM = 2, (2). dimM = 3, (3). \({dim M \geq 4}\)] and all the fibers are Ricci flat.

Some global properties of mixed super quasi-Einstein manifolds

Abstract: Within the framework of mixed super quasi-Einstein mani- folds, are proved three theorems: the flrst one shows that the compact orientable manifolds MS(QE)n (n ‚ 3) without boundary do not admit non-isometric conformal vector flelds, the second one provides a su-ciency condition for non-existence of nontrivial Killing vector flelds, and the last one characterizes the harmonic vector flelds under certain assumptions.

η-Ricci solitons on Lorentzian para-Sasakian manifolds

Abstract: We consider η-Ricci solitons on Lorentzian para-Sasakian manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0 and S · R(ξ,X) = 0. We prove that on a Lorentzian para-Sasakian manifold (M, φ, ξ, η, 1), if the Ricci curvature satisfies one of the previous conditions, the existence of η-Ricci solitons implies that (M, 1) is Einstein manifold. We also conclude that in these cases there is no Ricci soliton on M with the potential vector field ξ. On the other way, if M is of constant curvature, then (M, 1) is elliptic manifold. Cases when the Ricci tensor satisfies different other conditions are also discussed.

On quasi-Einstein spacetimes

Abstract: The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. For instance, the Robertson-Walker spacetimes are quasi-Einstein manifolds. The object of the present paper is to study quasi-Einstein spacetimes. Some basic geometric properties of such a spacetime are obtained. The applications of quasi-Einstein spacetimes in general relativity and cosmology are investigated. Finally, the existence of such spacetimes are ensured by several interesting examples.