On Hopf hypersurfaces of the complex hyperbolic 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_ | 1866915553538473984 |
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| author | Li, Haizhong Tamaru, Hiroshi Yao, Zeke |
| author_facet | Li, Haizhong Tamaru, Hiroshi Yao, Zeke |
| contents | In this paper, we study the Hopf hypersurfaces of the complex hyperbolic quadric $Q^{m*}=SO^o_{2,m}/(SO_2\times SO_m)$ ($m\geq3$) with constant principal curvatures. We classify the Hopf hypersurfaces of $Q^{m*}$ ($m\geq3$) with at most two distinct constant principal curvatures. For Hopf hypersurfaces with three or four distinct constant principal curvatures, we determine the values of the principal curvatures as well as their multiplicities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hopf hypersurfaces of the complex hyperbolic quadric with constant principal curvatures Li, Haizhong Tamaru, Hiroshi Yao, Zeke Differential Geometry 53C42, 53B25, 53C55 In this paper, we study the Hopf hypersurfaces of the complex hyperbolic quadric $Q^{m*}=SO^o_{2,m}/(SO_2\times SO_m)$ ($m\geq3$) with constant principal curvatures. We classify the Hopf hypersurfaces of $Q^{m*}$ ($m\geq3$) with at most two distinct constant principal curvatures. For Hopf hypersurfaces with three or four distinct constant principal curvatures, we determine the values of the principal curvatures as well as their multiplicities. |
| title | On Hopf hypersurfaces of the complex hyperbolic quadric with constant principal curvatures |
| topic | Differential Geometry 53C42, 53B25, 53C55 |
| url | https://arxiv.org/abs/2510.12284 |