Ricci solitons on singly warped product manifolds and applications

TL;DR

This paper investigates Ricci solitons on warped product manifolds, showing their factors are Ricci solitons, and explores specific cases involving conformal and concurrent vector fields, with applications to space-times.

Contribution

It establishes that Ricci solitons on warped products imply Ricci solitons on their factors and analyzes special cases with additional vector fields.

Findings

Factors of Ricci soliton warped products are Ricci solitons.

Characterization of Ricci solitons with conformal or concurrent vector fields.

Applications to warped product space-times.

Abstract

The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we study Ricci soliton on some warped product space-times.