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Kyungpook Mathematical Journal 2020; 60(3): 571-584

Published online September 30, 2020

Copyright © Kyungpook Mathematical Journal.

On Generalized Ricci Recurrent Spacetimes

Chiranjib Dey

Dhamla Jr. High School, Vill-Dhamla, P.O.-Kedarpur, Dist-Hooghly, Pin-712406, West Bengal, India
e-mail : dey9chiranjib@gmail.com

Received: December 5, 2018; Revised: March 24, 2020; Accepted: March 25, 2020

Abstract

The object of the present paper is to characterize generalized Ricci recurrent (GR4) spacetimes. Among others things, it is proved that a conformally flat GR4 spacetime is a perfect fluid spacetime. We also prove that a GR4 spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR4 spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR4 spacetime is non-empty and a GR4 spacetime is not a trivial case.

Keywords: generalized Ricci recurrent manifolds, conformally flatness