Hyperbolic Ricci soliton on warped product manifolds

Abstract

In this paper, we investigate hyperbolic Ricci soliton as the special solution of hyperbolic geometric flow on warped product manifolds. Then, especially, we study these manifolds admitting either a conformal vector field or a concurrent vector field. Also, the question that:" whether or not a hyperbolic soliton reduces to an Einstein manifold?" is considered and answered. Finally, we obtain some necessary conditions for generalized Robertson-Walker space-time to be a hyperbolic Ricci soliton.