O(2)-symmetry of 3D steady gradient Ricci solitons
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912280647565312 |
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| author | Lai, Yi |
| author_facet | Lai, Yi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01146 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | O(2)-symmetry of 3D steady gradient Ricci solitons Lai, Yi Differential Geometry 53E20 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. |
| title | O(2)-symmetry of 3D steady gradient Ricci solitons |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2205.01146 |