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In the present paper, we characterize m-dimensional ζ -conformally flat L P -Kenmotsu manifolds (briefly, (L P K) m ) equipped with the Ricci–Yamabe solitons (RYS) and gradient Ricci–Yamabe solitons (GRYS). It is proven that the scalar curvature r of an (L P K) m admitting an RYS satisfies the Poisson equation Δ r = 4 (m − 1) δ { β (m − 1) + ρ } + 2 (m − 3) r − 4 m (m − 1) (m − 2) , where ρ , δ (≠ 0) ∈ R . In this sequel, the condition for which the scalar curvature of an (L P K) m admitting an RYS holds the Laplace equation is established. We also give an affirmative answer for the existence of a GRYS on an (L P K) m . Finally, a non-trivial example of an L P -Kenmotsu manifold (L P K) of dimension four is constructed to verify some of our results. [ABSTRACT FROM AUTHOR]

The paper deals with the study of Z-symmetric manifolds (Z S) 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 (Z S) 4 spacetimes admitting Codazzi type Schouten tensor. Finally, we construct an example of (Z S) 4 to verify our result. [ABSTRACT FROM AUTHOR]

In the present article, some geometric and physical properties of M G (Q E) n were investigated. Moreover, general relativistic viscous fluid M G (Q E) 4 spacetimes with some physical applications were studied. Finally, through a non-trivial example of M G (Q E) 4 spacetime, we proved its existence. [ABSTRACT FROM AUTHOR]

In this note, the generalized Lorentzian Sasakian-space-form M 1 2 n + 1 (f 1 , f 2 , f 3) satisfying certain constraints on the M -projective curvature tensor W * is considered. Here, we characterize the structure M 1 2 n + 1 (f 1 , f 2 , f 3) when it is, respectively, M -projectively flat, M -projectively semisymmetric, M -projectively pseudosymmetric, and φ − M -projectively semisymmetric. Moreover, M 1 2 n + 1 (f 1 , f 2 , f 3) satisfies the conditions W * (ζ , V 1) · S = 0 , W * (ζ , V 1) · R = 0 and W * (ζ , V 1) · W * = 0 are also examined. Finally, illustrative examples are given for obtained results. [ABSTRACT FROM AUTHOR]