Some geometric and physical properties of pseudo m*-projective symmetric manifolds

Abstract

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 ? 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.