Geodesic
Characterizations of a spacetime admitting ψ-conformal curvature tensor
Filomat, Tome 37 (2023) no. 30, p. 10265

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DOI

In this paper, we introduce Ψ-conformal curvature tensor, a new tensor that generalizes the conformal curvature tensor. At first, we deduce a few fundamental geometrical properties of Ψ-conformal curvature tensor and pseudo Ψ-conharmonically symmetric manifolds and produce some interesting outcomes. Moreover, we study Ψ-conformally flat perfect fluid spacetimes. As a consequence, we establish a number of significant theorems about Minkowski spacetime, GRW-spacetime, projective collineation. Moreover, we show that if a Ψ-conformally flat spacetime admits a Ricci bi-conformal vector field, then it is either conformally flat or of Petrov type N. At last, we consider pseudo Ψ conformally symmetric spacetime admitting harmonic Ψ-conformal curvature tensor and prove that the semi-symmetric energy momentum tensor and Ricci semi-symmetry are equivalent and also, the Ricci collineation and matter collineation are equivalent.
DOI : 10.2298/FIL2330265M
Classification : 83D05, 83C05, 53C15, 53C50
Keywords: Ψ-conformal curvature tensor, Pseudo Ψ-conformally symmetric manifolds, Ψ-conformally flat spacetime 
Fatemah Mofarreh; Krishnendu De; Uday C; and De. Characterizations of a spacetime admitting ψ-conformal curvature tensor. Filomat, Tome 37 (2023) no. 30, p. 10265 . doi: 10.2298/FIL2330265M
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     title = {Characterizations of a spacetime admitting \ensuremath{\psi}-conformal curvature tensor},
     journal = {Filomat},
     pages = {10265 },
     year = {2023},
     volume = {37},
     number = {30},
     doi = {10.2298/FIL2330265M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2330265M/}
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