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.