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http://dx.doi.org/10.5666/KMJ.2020.60.3.571

On Generalized Ricci Recurrent Spacetimes  

Dey, Chiranjib (Dhamla Jr. High School)
Publication Information
Kyungpook Mathematical Journal / v.60, no.3, 2020 , pp. 571-584 More about this Journal
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;
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