Some rigidity results on shrinking gradient Ricci soliton
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916476475146240 |
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| author | Ou, Jianyu Qu, Yuanyuan Wu, Guoqiang |
| author_facet | Ou, Jianyu Qu, Yuanyuan Wu, Guoqiang |
| contents | Suppose $(M^n, g, f)$ is a complete shrinking gradient Ricci soliton. We give several rigidity results under some natural conditions, generalizing the results in \cite{Petersen-Wylie,Guan-Lu-Xu}. Using maximum principle, we prove that shrinking gradient Ricci soliton with constant scalar curvature $R=1$ is isometric to a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$, giving a new proof of the main results of Cheng-Zhou \cite{Cheng-Zhou}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some rigidity results on shrinking gradient Ricci soliton Ou, Jianyu Qu, Yuanyuan Wu, Guoqiang Differential Geometry Suppose $(M^n, g, f)$ is a complete shrinking gradient Ricci soliton. We give several rigidity results under some natural conditions, generalizing the results in \cite{Petersen-Wylie,Guan-Lu-Xu}. Using maximum principle, we prove that shrinking gradient Ricci soliton with constant scalar curvature $R=1$ is isometric to a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$, giving a new proof of the main results of Cheng-Zhou \cite{Cheng-Zhou}. |
| title | Some rigidity results on shrinking gradient Ricci soliton |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.06395 |