Z-symmetric manifold admitting concircular Ricci symmetric tensor

Abstract

This paper deals with Z-symmetric Riemannian manifolds with concircular Ricci symmetric tensor. In the first section, we give an introduction of Z-symmetric manifold. In the second section, the definition of concircular Ricci symmetric tensor is given. In the third section, we introduce Z-symmetric Riemannian manifold admitting concircular Ricci symmetric tensor and we examine some properties of these manifolds. In the last section, we study Z-symmetric spacetimes admitting concircular Ricci symmetric tensor and we give two examples for the existence of these manifolds.