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arXiv · 2210.01945

Rigidity results for shrinking and expanding Ricci solitons

Benedito Leandro·Jeferson Poveda
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Abstract

In this paper, we prove some rigidity results for both shrinking and expanding Ricci solitons. First, we prove that compact shrinking Ricci solitons are Einstein if we control the maximum value of the potential function. Then, we prove some rigidity results for non-compact gradient expanding and shrinking Ricci solitons with pinched Ricci and scalar curvatures, assuming an asymptotic condition on the scalar curvature at infinity.

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Benedito Leandro, Jeferson Poveda. 2022-10-04. Rigidity results for shrinking and expanding Ricci solitons. https://arxiv.org/abs/2210.01945

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