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.

Deformation of curvature tensors under conformal Ricci flow

Abstract: In this paper we find out the deformation of curvature tensor and Ricci tensor as the metric varies in conformal Ricci flow.

Characterization on Mixed Generalized Quasi-Einstein Manifold

Abstract: In the present paper we study characterizations of odd and even dimensional mixed generalized quasi-Einstein manifold. Next we prove that a mixed generalized quasi-Einstein manifold is a generalized quasi-Einstein manifold under a certain condition. Then we obtain three and four dimensional examples of mixed generalized quasi-Einstein manifold to ensure the existence of such manifold. Finally we establish the examples of warped product on mixed generalized quasi-Einstein manifold.

Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection

Abstract: The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection.

A characterization of warped product on mixed super quasi-einstein manifold

Abstract: In this paper we investigate the expressions of the Ricci tensors and scalar curvatures of warped product manifold with respect to the bases and fibres when warped product manifold is a mixed super quasi-Einstein manifold. In some cases we give some obstructions to the existence of such manifolds and in the last section we give an example of warped product on mixed super quasi-Einstein manifold.

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.