Semi-Symmetric Curvature Properties of Robertson-Walker Spacetimes

초록

The aim of the present paper is to characterize Robertson-Walker (RW) spacetimes satisfying certain curvature conditions. A necessary and suffi-cient condition for a RW spacetime to be Ricci semisymmetric is given. We prove that a four-dimensional Ricci symmetric RW spacetime is vacuum. We also study the properties of projective collineation and matter collineation within the framework of a four-dimensional Ricci symmetric RW spacetime. Among others, it is proved that a Lorentzian manifold of dimension n > 3 is a RW spacetime if and only if the spacetime is of quasi-constant curvature. Finally, some new characteristics of RW spacetimes are obtained.

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