On generalized projective P-curvature tensor

The object of the present paper is to introduce and investigate the P-curvature tensor that generalizes projective, conharmonic, M-projective and the set of Wi curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P-curvature tenso...

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Bibliographic Details
Published in:Journal of geometry and physics 2021-01, Vol.159, p.103952, Article 103952
Main Authors: De, Uday Chand, Abu-Donia, H.M., Shenawy, Sameh, Syied, Abdallah Abdelhameed
Format: Article
Language:English
Subjects:
[formula omitted]-curvature tensor
Einstein’s field equation
Energy–momentum tensor
Perfect fluid spacetime
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Summary:The object of the present paper is to introduce and investigate the P-curvature tensor that generalizes projective, conharmonic, M-projective and the set of Wi curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P-curvature tensor are Einstein and those admitting flat P-curvature tensor has a constant curvature. Classification theorems for pseudo-Riemannian manifolds admitting a divergence-free P-curvature tensor are given in each subspace of Gray’s decomposition of the covariant derivative of the Ricci tensor. Space–times having a flat P-curvature tensor or a divergence free P-curvature tensor are scrutinized. Finally, perfect fluid space–times admitting various features of the P-curvature tensor are considered.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2020.103952