On Warped product gradient Ricci Soliton

Márcio Lemes de Sousa; Romildo Pina

On Warped product gradient Ricci Soliton

Differential Geometry 2016-04-18 v2

Authors: Márcio Lemes de Sousa , Romildo Pina

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.

Keywords

warped product gradient Ricci soliton Einstein manifold potential function steady soliton pseudo-Euclidean space Ricci-flat fiber

Cite

@article{arxiv.1505.03833,
  title  = {On Warped product gradient Ricci Soliton},
  author = {Márcio Lemes de Sousa and Romildo Pina},
  journal= {arXiv preprint arXiv:1505.03833},
  year   = {2016}
}

Comments

we made a change in the proof of Theorem 1.1

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