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Z-symmetric manifold admitting concircular Ricci symmetric tensor. (English) Zbl 07274468
Summary: 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.
MSC:
53B20 Local Riemannian geometry
53B21 Methods of local Riemannian geometry
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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