Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

Fei He

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arXiv · 1311.4515

Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

Fei He

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Abstract

Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.

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Fei He. 2013-11-18. Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds. https://arxiv.org/abs/1311.4515

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