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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09727 |
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| _version_ | 1866911053773799424 |
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| author | Guan, Pengfei Yuan, Yu |
| author_facet | Guan, Pengfei Yuan, Yu |
| contents | We prove that the normalized second fundamental form $A$ of immersed $C^2$ hypersurface in a space form $(N^{n+1}, \bar g)$ is intrinsic provided $σ_{2k+1}(A)\neq 0$ for some $k\ge 1$. We also establish the intrinsicality of the normalized second fundamental form $A$ of $M^{n}=\partialΩ$ for domain $ Ω\subset N^{n+1}, \ n\ge 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsicality of second fundamentals of hypersurfaces in space form Guan, Pengfei Yuan, Yu Differential Geometry 53A05, 53C24 We prove that the normalized second fundamental form $A$ of immersed $C^2$ hypersurface in a space form $(N^{n+1}, \bar g)$ is intrinsic provided $σ_{2k+1}(A)\neq 0$ for some $k\ge 1$. We also establish the intrinsicality of the normalized second fundamental form $A$ of $M^{n}=\partialΩ$ for domain $ Ω\subset N^{n+1}, \ n\ge 3$. |
| title | Intrinsicality of second fundamentals of hypersurfaces in space form |
| topic | Differential Geometry 53A05, 53C24 |
| url | https://arxiv.org/abs/2507.09727 |