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arXiv · 2205.01146

O(2)-symmetry of 3D steady gradient Ricci solitons

Yi Lai
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Abstract

For any 3D steady gradient Ricci soliton with positive curvature, we prove that it must be isometric to the Bryant soliton if it is asymptotic to a ray. Otherwise, it is asymptotic to a sector and hence a flying wing. We show that all 3D flying wings are O(2)-symmetric. Therefore, all 3D steady gradient Ricci solitons are O(2)-symmetric.

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Yi Lai. 2022-05-02. O(2)-symmetry of 3D steady gradient Ricci solitons. https://doi.org/10.2140/gt.2025.29.687

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