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arXiv · 1109.0243

On the global structure of conformal gradient solitons with nonnegative Ricci tensor

Giovanni Catino·Carlo Mantegazza·Lorenzo Mazzieri
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Abstract

In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean space $\mathbb{R}^{n}$ or to the round sphere $\mathbb{S}^{n}$. In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.

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Giovanni Catino, Carlo Mantegazza, Lorenzo Mazzieri. 2011-09-01. On the global structure of conformal gradient solitons with nonnegative Ricci tensor. https://arxiv.org/abs/1109.0243

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