On Warped product gradient Ricci Soliton

Márcio Lemes de Sousa; Romildo Pina

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arXiv · 1505.03833

On Warped product gradient Ricci Soliton

Márcio Lemes de Sousa·Romildo Pina

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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.

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Márcio Lemes de Sousa, Romildo Pina. 2015-05-14. On Warped product gradient Ricci Soliton. https://arxiv.org/abs/1505.03833

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