Rigidity of closed minimal hypersurface in $\mathbb{S}^5$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929558305898496 |
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| author | Cheng, Pengpeng Li, Tongzhu |
| author_facet | Cheng, Pengpeng Li, Tongzhu |
| contents | Let $M^4\to \mathbb{S}^5$ be a closed immersed minimal hypersurface with constant squared length of the second fundamental form $S$ in a $5$-dimensional sphere $\mathbb{S}^5$. In this paper, we prove that if $3$-mean curvature $H_3$ and the number $g$ of the distinct principal curvatures are constant, then $M^4$ is an isoparametric hypersurface, and the value of $S$ can only be $0, 4, 12$. This result supports Chern Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of closed minimal hypersurface in $\mathbb{S}^5$ Cheng, Pengpeng Li, Tongzhu Differential Geometry Let $M^4\to \mathbb{S}^5$ be a closed immersed minimal hypersurface with constant squared length of the second fundamental form $S$ in a $5$-dimensional sphere $\mathbb{S}^5$. In this paper, we prove that if $3$-mean curvature $H_3$ and the number $g$ of the distinct principal curvatures are constant, then $M^4$ is an isoparametric hypersurface, and the value of $S$ can only be $0, 4, 12$. This result supports Chern Conjecture. |
| title | Rigidity of closed minimal hypersurface in $\mathbb{S}^5$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.19531 |