Rotational symmetry of complete shrinking gradient Yamabe solitons
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917383110656000 |
|---|---|
| author | Maeta, Shun |
| author_facet | Maeta, Shun |
| contents | In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally symmetric. This assumption is optimal for higher dimensions. This result resolves the Yamabe-soliton analogue of Perelman's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09166 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rotational symmetry of complete shrinking gradient Yamabe solitons Maeta, Shun Differential Geometry 53C21, 53C25, 53C20 In this paper, we show that any nontrivial complete shrinking gradient Yamabe soliton whose scalar curvature is bounded below by the soliton constant everywhere and is strictly greater than the constant at some point is rotationally symmetric. This assumption is optimal for higher dimensions. This result resolves the Yamabe-soliton analogue of Perelman's conjecture. |
| title | Rotational symmetry of complete shrinking gradient Yamabe solitons |
| topic | Differential Geometry 53C21, 53C25, 53C20 |
| url | https://arxiv.org/abs/2309.09166 |