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This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic. [ABSTRACT FROM AUTHOR]

This study aims at examining the effects of an almost Ricci–Bourguignon soliton structure on the base and fiber factor manifolds of a doubly warped product manifold. First, a number of preconditions and sufficiency criteria for an almost Ricci–Bourguignon soliton doubly warped product are addressed. Additionally, an almost Ricci–Bourguignon soliton on doubly warped product manifolds admitting a conformal vector field is taken into consideration. Finally, how the almost Ricci–Bourguignon soliton behaves in doubly warped product space–times is examined. [ABSTRACT FROM AUTHOR]

Generalized Ricci recurrent spacetimes (GR) n are investigated in Gray's seven subspaces. It is proved that a (GR) n spacetime in all subspaces but one is an Einstein spacetime. The subspace ℐ cannot contain a (GR) n spacetime. Further, the subspaces ℐ ⊕ A and ℐ ⊕ B reduce to A and B , respectively. Next, we prove that a (GR) n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein or the vector field Al is closed. Further, it is shown that the Ricci tensor of (GR) n is Riemann compatible if Al is closed. Finally, sufficient conditions are given on a (GR) n warped product manifold to guarantee that the factor manifolds are Einstein. Moreover, it is shown that a generalized Ricci recurrent GRW spacetime is an Einstein spacetime. [ABSTRACT FROM AUTHOR]

In this paper, warped product mixed generalized quasi-Einstein manifolds MG(QE) n are studied. It is shown that a Ricci recurrent MG(QE) n manifold is a product manifold whose factors are Ricci recurrent. Sufficient conditions for a MG(QE) n to be a G(QE) n are derived. Then, we classify three types of warped product MG(QE) n . For example, it is proved that the fiber manifold is Einstein in the first type, (QE) n in the second type and MG(QE) n in the third type. [ABSTRACT FROM AUTHOR]

Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M , g , f , μ to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a λ , n + m -Einstein manifold M , g , w having harmonic Weyl tensor, ∇ j w ∇ m w C j k l m = 0 and ∇ l w ∇ l w < 0 reduces to a perfect fluid generalized Robertson–Walker spacetime with Einstein fibers. Finally, M , g , w reduces to a perfect fluid manifold if φ = − m ∇ ln w is a φ R i c -vector field on M and to an Einstein manifold if ψ = ∇ w is a ψ R i c -vector field on M. Some consequences of these results are considered. [ABSTRACT FROM AUTHOR]

Recently, it is proven that generalized Robertson–Walker space-times in all orthogonal subspaces of Gray's decomposition except one (unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a constant scalar curvature. It is shown that generalized quasi-Einstein GRW space-times reduce to Einstein space-times or perfect fluid space-times. [ABSTRACT FROM AUTHOR]

The object of the present paper is to introduce and investigate the P -curvature tensor that generalizes projective, conharmonic, M -projective and the set of W i curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P -curvature tensor are Einstein and those admitting flat P -curvature tensor has a constant curvature. Classification theorems for pseudo-Riemannian manifolds admitting a divergence-free P -curvature tensor are given in each subspace of Gray's decomposition of the covariant derivative of the Ricci tensor. Space–times having a flat P -curvature tensor or a divergence free P -curvature tensor are scrutinized. Finally, perfect fluid space–times admitting various features of the P -curvature tensor are considered. [ABSTRACT FROM AUTHOR]