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.
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