On Hopf hypersurfaces of the complex quadric with constant principal curvatures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917997929562112 |
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| author | Li, Haizhong Tamaru, Hiroshi Yao, Zeke |
| author_facet | Li, Haizhong Tamaru, Hiroshi Yao, Zeke |
| contents | In this paper, we classify the Hopf hypersurfaces of the complex quadric $Q^m=SO_{m+2}/(SO_2SO_m)$ ($m\geq3$) with at most five distinct constant principal curvatures. We also classify the Hopf hypersurfaces of $Q^m$ ($m=3,4,5$) with constant principal curvatures. All these real hypersurfaces are open parts of homogeneous examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hopf hypersurfaces of the complex quadric with constant principal curvatures Li, Haizhong Tamaru, Hiroshi Yao, Zeke Differential Geometry 53C42, 53B25, 53C55 In this paper, we classify the Hopf hypersurfaces of the complex quadric $Q^m=SO_{m+2}/(SO_2SO_m)$ ($m\geq3$) with at most five distinct constant principal curvatures. We also classify the Hopf hypersurfaces of $Q^m$ ($m=3,4,5$) with constant principal curvatures. All these real hypersurfaces are open parts of homogeneous examples. |
| title | On Hopf hypersurfaces of the complex quadric with constant principal curvatures |
| topic | Differential Geometry 53C42, 53B25, 53C55 |
| url | https://arxiv.org/abs/2504.17689 |