ρ‐Einstein Solitons on Warped Product Manifolds and Applications

Abstract

The purpose of this research is to investigate how a ρ-Einstein soliton structure on a warped product manifold affects its base and fiber factor manifolds. Firstly, the pertinent properties of ρ-Einstein solitons are provided. Secondly, numerous necessary and sufficient conditions of a ρ-Einstein soliton warped product manifold to make its factor ρ-Einstein soliton are examined. On a ρ-Einstein gradient soliton warped product manifold, necessary and sufficient conditions for making its factor ρ-Einstein gradient soliton are presented. ρ-Einstein solitons on warped product manifolds admitting a conformal vector field are also considered. Finally, the structure of ρ-Einstein solitons on some warped product space-times is investigated.

Projective Collineations in Warped Product Manifolds and (PRS)n Manifolds

“…Generalized Robertson-Walker space-time [22][23][24] I × f M 2 and standard static space-time [25][26][27] M 1 × f I are exceptional cases of Lorentzian warped product manifolds when a factor manifold is an open, connected interval of the real line. Warped product manifolds' scalar curvatures, Ricci curvatures, and Riemann curvatures can all be described in terms of the lift of the relevant curvature tensors from the factor manifolds to the product manifold [28][29][30].…”

Ricci Solitons on Multiply Warped Product Manifolds

“…Doubly, multiply and sequential warped product manifolds are known generalizations of the warped product manifolds ( [11], [29], [30]). There are many papers in which Ricci solitons on some Riemannian manifolds or on warped product manifolds or on some generalizations of warped products have been studied, for example see ( [1], [4], [12], [16], [20], [21], [25], [26], [28], [33]). By a motivation from the above studies, in this paper, we consider Ricci-Bourguignon solitons on sequential warped product manifolds which is an another generalization of the warped product manifolds.…”