On pseudo H-symmetric Lorentzian manifolds with applications to relativity

Abstract

In this paper, we introduce a new type of curvature tensor named H-curvature tensor of type (1, 3) which is a linear combination of conformal and projective curvature tensors. First we deduce some basic geometric properties of H-curvature tensor. It is shown that a H-flat Lorentzian manifold is an almost product manifold. Then we study pseudo H-symmetric manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian manifolds. Also, we provide several interesting results. Among others, we prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar curvature of the manifold vanishes and conversely. Moreover, we deal with pseudo H-symmetric perfect fluid spacetimes and obtain several interesting results. Also, we present some results of the spacetime satisfying divergence free H-curvature tensor. Finally, we construct a non-trivial Lorentzian metric of (PHS)4.

Spacetimes admitting the Z-symmetric tensor

“…Thus we have Riem•Riem = hQ(g, Riem) for some smooth function h. This paper deals with Chaki's notion of pseudosymmetric. Pseudosymmetric manifolds have been studied by several authors such as ( [11], [12], [17], [25]) and others.…”

Characterizations of -flat curvature tensor on spacetimes and f(r,T) -gravity

“…). De et al [20] introduced -curvature tensor of 1, 3 ( )type which is the linear combination of  and  defined by…”