Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912463767732224 |
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| author | Li, Fengjiang Ou, Jianyu Qu, Yuanyuan Wu, Guoqiang |
| author_facet | Li, Fengjiang Ou, Jianyu Qu, Yuanyuan Wu, Guoqiang |
| contents | Let $(M, g, f)$ be a $5$-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= λg$, where $\text{Ric}$ is the Ricci tensor and $\nabla^2f$ is the Hessian of the potential function $f$. We prove that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^3$ if $M$ has constant scalar curvature $R=3 λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature Li, Fengjiang Ou, Jianyu Qu, Yuanyuan Wu, Guoqiang Differential Geometry Let $(M, g, f)$ be a $5$-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= λg$, where $\text{Ric}$ is the Ricci tensor and $\nabla^2f$ is the Hessian of the potential function $f$. We prove that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^3$ if $M$ has constant scalar curvature $R=3 λ$. |
| title | Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.10712 |