Ricci solitons on spacetimes with the spatially homogeneous rotating metrics

Abstract

This paper investigates Ricci solitons on spacetimes equipped with spatially homogeneous rotating metrics. We systematically classify all vector fields that generate Ricci solitons within this geometric framework. Special attention is devoted to identifying the precise conditions under which these vector fields assume gradient form. Furthermore, we establish that every vector field associated with a Ricci soliton in this setting exhibits conformal Killing properties, revealing a fundamental connection between these geometric structures. Finally, we present an example of the desired space and examine the Ricci solitons on it.