Doubly warped product manifolds with the structure of hyperbolic Ricci solitons

Abstract In this paper we study hyperbolic Ricci solitons on doubly warped product manifolds. The necessary conditions are obtained for a hyperbolic Ricci soliton with the structure of a doubly warped product to be an Einstein manifold when we consider the potential field as a Killing or a conformal vector field. Also, we examined the behavior of hyperbolic Ricci solitons on doubly warped product space-times.