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.

In the present article, some geometric and physical properties of MG(QE)n were investigated. Moreover, general relativistic viscous fluid MG(QE)4 spacetimes with some physical applications were studied. Finally, through a non-trivial example of MG(QE)4 spacetime, we proved its existence.

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In this paper we study mixed generalized quasi-Einstein manifold satisfying some curvature conditions like K.Ric = 0, C.Ric = 0, N.Ric = 0, where K, Ric, C and N denote the Reimannian curvature tensor, Ricci tensor, conformal curvature tensor and concircular curvature tensor and obtain some interesting and fruitful results on it.

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