1. Pseudo B-symmetric manifolds.
- Author
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Suh, Young Jin, Mantica, Carlo Alberto, De, Uday Chand, and Pal, Prajjwal
- Subjects
TENSOR algebra ,RIEMANNIAN manifolds ,MANIFOLDS (Mathematics) ,MATHEMATICAL symmetry ,SYMMETRIC functions - Abstract
In this paper, we introduce a new tensor named -tensor which generalizes the -tensor introduced by Mantica and Suh [Pseudo symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. Then, we study pseudo--symmetric manifolds which generalize some known structures on pseudo-Riemannian manifolds. We provide several interesting results which generalize the results of Mantica and Suh [Pseudo symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Methods Mod. Phys. 9(1) (2012) 1250004]. At first, we prove the existence of a . Next, we prove that a pseudo-Riemannian manifold is -semisymmetric if and only if it is Ricci-semisymmetric. After this, we obtain a sufficient condition for a to be pseudo-Ricci symmetric in the sense of Deszcz. Also, we obtain the explicit form of the Ricci tensor in a if the -tensor is of Codazzi type. Finally, we consider conformally flat pseudo--symmetric manifolds and prove that a spacetime is a -wave under certain conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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