Complete hypersurfaces in $R^{n+1}$ with constant mean and scalar curvature
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917172211613696 |
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| author | Ge, Jianquan Tao, Ya |
| author_facet | Ge, Jianquan Tao, Ya |
| contents | In this paper, we investigate the rigidity problems of complete hypersurfaces with constant mean curvature and constant scalar curvature in Euclidean spaces. Firstly, under some conditions of Gaussian-Kronecker curvature, we provide characterizations for the unsolved cases of Núñez's theorems in dimensions 4 and 5, as well as several rigidity results under some conditions of $r$-th mean curvatures. Moreover, for the case of dimension 6, we also present analogous rigidity results. Finally, for general dimensions, we offer a rigidity theorem under similar pinching conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete hypersurfaces in $R^{n+1}$ with constant mean and scalar curvature Ge, Jianquan Tao, Ya Differential Geometry In this paper, we investigate the rigidity problems of complete hypersurfaces with constant mean curvature and constant scalar curvature in Euclidean spaces. Firstly, under some conditions of Gaussian-Kronecker curvature, we provide characterizations for the unsolved cases of Núñez's theorems in dimensions 4 and 5, as well as several rigidity results under some conditions of $r$-th mean curvatures. Moreover, for the case of dimension 6, we also present analogous rigidity results. Finally, for general dimensions, we offer a rigidity theorem under similar pinching conditions. |
| title | Complete hypersurfaces in $R^{n+1}$ with constant mean and scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.22598 |