English

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

Differential Geometry 2025-03-19 v3

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.

Keywords

Cite

@article{arxiv.2205.01146,
  title  = {O(2)-symmetry of 3D steady gradient Ricci solitons},
  author = {Yi Lai},
  journal= {arXiv preprint arXiv:2205.01146},
  year   = {2025}
}