1. GRAY's DECOMPOSITION AND WARPED PRODUCT OF GENERALIZED RICCI RECURRENT SPACETIMES.
- Author
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Chand De, Uday, Shenawy, Sameh, and Syied, Abdallah Abdelhameed
- Subjects
- *
EINSTEIN manifolds , *VECTOR fields , *SPACETIME - Abstract
Generalized Ricci recurrent spacetimes (GR) n are investigated in Gray's seven subspaces. It is proved that a (GR) n spacetime in all subspaces but one is an Einstein spacetime. The subspace ℐ cannot contain a (GR) n spacetime. Further, the subspaces ℐ ⊕ A and ℐ ⊕ B reduce to A and B , respectively. Next, we prove that a (GR) n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein or the vector field Al is closed. Further, it is shown that the Ricci tensor of (GR) n is Riemann compatible if Al is closed. Finally, sufficient conditions are given on a (GR) n warped product manifold to guarantee that the factor manifolds are Einstein. Moreover, it is shown that a generalized Ricci recurrent GRW spacetime is an Einstein spacetime. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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