Z-Symmetric Manifolds Admitting Schouten Tensor

Abstract

The paper deals with the study of Z-symmetric manifolds (ZS)n admitting certain cases of Schouten tensor (specifically: Ricci-recurrent, cyclic parallel, Codazzi type and covariantly constant), and investigate some geometric and physical properties of the manifold. Moreover, we also study (ZS)4 spacetimes admitting Codazzi type Schouten tensor. Finally, we construct an example of (ZS)4 to verify our result.

Keywords

• schouten tensor
• Z-symmetric tensor
• codazzi type tensor
• Z symmetric spacetimes