On Warped product gradient Ricci Soliton

Abstract

In this paper we consider $M=B{\times }_{f}F$ warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber $F$ is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an $n$-dimensional pseudo-Euclidean space, invariant under the action of an $(n-1)$-dimensional translation group and the fiber $F$ is Ricci-flat.

we made a change in the proof of Theorem 1.1

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