Geodesic
Some geometric and physical properties of pseudo m * -projective symmetric manifolds
Filomat, Tome 37 (2023) no. 8, p. 2465

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DOI

In this study we introduce a new tensor in a semi-Riemannian manifold, named the M *-projective curvature tensor which generalizes the m-projective curvature tensor. We start by deducing some fundamental geometric properties of the M *-projective curvature tensor. After that, we study pseudo M *-projective symmetric manifolds (PM * S) n. A non-trivial example has been used to show the existence of such a manifold. We introduce a series of interesting conclusions. We establish, among other things, that if the scalar curvature ρ is non-zero, the associated 1-form is closed for a (PM * S) n with divM * = 0. We also deal with pseudo M *-projective symmetric spacetimes, M *-projectively flat perfect fluid spacetimes, and M *-projectively flat viscous fluid spacetimes. As a result, we establish some significant theorems.
DOI : 10.2298/FIL2308465H
Classification : 53B30, 53C25, 53C50
Keywords: M∗-projective curvature tensor, pseudo M∗-projective symmetric manifolds, perfect fluid, viscous fluid, energy- momentum tensor, Einstein’s field equation 
Dipankar Hazra; Uday C; and De; Sameh Shenawy; Abdallah Abdelhameed Syied. Some geometric and physical properties of pseudo m * -projective symmetric manifolds. Filomat, Tome 37 (2023) no. 8, p. 2465 . doi: 10.2298/FIL2308465H
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     author = {Dipankar Hazra and Uday C and and De and Sameh Shenawy and Abdallah Abdelhameed Syied},
     title = {Some geometric and physical properties of pseudo m * -projective symmetric manifolds},
     journal = {Filomat},
     pages = {2465 },
     year = {2023},
     volume = {37},
     number = {8},
     doi = {10.2298/FIL2308465H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2308465H/}
}
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