Characterizations of a spacetime admitting ψ-conformal curvature tensor


Fatemah Mofarreh, Krishnendu De, Uday Chand De




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.