Hyperbolic Ricci solitons on twisted warped product manifolds with some physical applications

Abstract

This paper examines the behavior of Ricci solitons within the framework of hyperbolic geometric flow on twisted warped product manifolds. By studying the influence of conformal and concurrent vector fields, we establish conditions under which these solitons reduce to Einstein manifolds, particularly when the warping function is constant or satisfies specific criteria. The analysis reveals that concurrent vector fields lead to Ricci-flat structures in both the base and fiber components, while Ricci bi-conformal vector fields introduce new geometric constraints. These results deepen the understanding of how curvature and flow dynamics interact in product manifolds, with potential implications for theoretical physics and differential geometry. The study provides foundational insights for future explorations of geometric evolution equations and their applications in mathematical cosmology.