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.

Conformal Einstein soliton within the framework of para-K$\"{a}$hler manifold

Abstract: The object of the present paper is to study some properties of para-K$a$hler manifold whose metric is conformal Einstein soliton. We have studied some certain curvature properties of para-K$a$hler manifold admitting conformal Einstein soliton.

Second order parallel tensor in trans-Sasakian manifolds and connection with Ricci soliton

Abstract: In this paper we have solved the Eisenhart problem for the symmetric case in the trans-Sasakian manifold of type (α, β) with non-vanishing ξ-sectional curvature and studied some of its consequences. Then we apply our result to obtain a Ricci soliton and studied its behavior for a particular case. Finally we studied the possible consequence for an affine Killing vector field.

Volume of a tetrahedron revisited

Abstract: Abstract The volume of a tetrahedron is represented in terms of the twelve face angles, inradii of the faces of tetrahedron, circumradii of the faces and the radius of the sphere circumscribing the tetrahedron

Multiply warped products quasi-Einstein manifolds with quarter-symmetric connection

Abstract: In this paper we study warped products and multiply warped products on quasi-Einstein manifolds with a quarter-symmetric connection. Then we apply our results to generalize Robertson-Walker spacetime with a quarter-symmetric connection.

The Fischer-Marsden Solutions on Almost CoKähler Manifold

Abstract: In this paper, we characterize the solutions of the Fischer-Marsden equation Lg(λ) = 0 on an almost CoKähler manifold. We prove that the Fischer-Marsden equation has only trivial solution on almost CoKähler manifold of dimension greater than 3 with ξ belonging to the (κ, μ)-nullity distribution and κ < 0.

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.