On weakly cyclic Z symmetric spacetimes

Abstract

The object of the present paper is to study weakly cyclic Z symmetric spacetimes. At first we prove that a weakly cyclic Z symmetric spacetime is a quasi Einstein spacetime. Then we study (W CZS) 4 spacetimes satisfying the condition div C = 0. Next we consider conformally flat (W CZS) 4 spacetimes. Finally, we characterise dust fluid and viscous fluid (W CZS) 4 spacetimes.

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

“…The findings presented in this study hold great significance for geometers in their future research endeavors. For example, these results can be applied to various types of space-times, such as Z recurrent space-times [49], almost pseudo Z symmetric space-times [11], weakly Z symmetric space-times [66], and weakly cyclic Z symmetric space-times [47,48].…”

On Z-Symmetric Manifold Admitting Projective Curvature Tensor

“…This manifold has received a great deal of attention and is studied in considerable detail by many authors [26][27][28][29][30][31][32][33]. Motivated by the above studies, in the present, we examine the properties of the Z-tensor of a Riemannian manifold admitting the projective curvature tensor.…”

Z-Symmetric Manifolds Admitting Schouten Tensor

“…By virtue of ( 37) and (41) and the fact that Z-symmetric tensor is covariantly constant, the relation (38) reduces to 4k(∇ U p)φ(Y)φ(V) + k(∇ U p)g(Y, V) = 0, which by taking Y = V = ξ and using (30) leads to ∇ U p = 0, i.e., the isotropic pressure p is constant. Thus from (37), we lead to ∇ U σ = 0, i.e., the energy density is constant. This completes the proof.…”