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

被引：0
作者：
Lai, Yi [1 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
GEOMETRY & TOPOLOGY | 2025年 / 29卷 / 02期
关键词：
CONVEX ANCIENT SOLUTIONS; MEAN-CURVATURE FLOW; LONG-TIME BEHAVIOR; ROTATIONAL SYMMETRY; CLASSIFICATION; UNIQUENESS; SHRINKING; RIGIDITY; FAMILY;
D O I：
10.2140/gt.2025.29.687
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that all 3D steady gradient Ricci solitons are O.2/-symmetric. The O.2/-symmetry is the most universal symmetry in Ricci flows with any type of symmetries. Our theorem is also the first instance of symmetry theorem for Ricci flows that are not rotationally symmetric. We also show that the Bryant soliton is the unique 3D steady gradient Ricci soliton with positive curvature that is asymptotic to a ray.
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收藏
页码：687 / 789
页数：104
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