Search

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]

In this work, generalized weakly ℋ -symmetric space-times (GWHS) n are investigated, where ℋ is any symmetric (0 , 2) tensor. It is proved that, in a nontrivial (GWHS) n space-time, the tensor ℋ has a perfect fluid form. Accordingly, sufficient conditions for a nontrivial generalized weakly Ricci symmetric space-time (GWRS) n to be either an Einstein space-time or a perfect fluid space-time are obtained. Also, conditions for space-times admitting either a generalized weakly symmetric energy-momentum tensor or a generalized weakly symmetric tensor to be Einstein or perfect fluid space-times are provided. [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]

The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ = ζ 1 + ζ 2 are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse's problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci symmetric space-times admitting projective collineations are investigated. [ABSTRACT FROM AUTHOR]

A conformally flat GRW space-time is a perfect fluid RW space-time. In this note, we investigated the influence of many differential curvature conditions, such as the existence of recurrent and semi-symmetric curvature tensors. In each case, the form of the Ricci curvature tensor, the energy–momentum tensor, the energy density, the pressure of the fluid, and the equation of state are determined and interpreted. For example, it is demonstrated that a Ricci semi-symmetric RW space-time reduces to Einstein space-time or a Ricci recurrent RW space-time, and the perfect fluid space-time is referred to as Yang pure space-time or dark matter era. [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]