Isoparametric Hypersurfaces in Products of Simply Connected Space Forms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915621138071552 |
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| author | de Lima, Ronaldo F. Pipoli, Giuseppe |
| author_facet | de Lima, Ronaldo F. Pipoli, Giuseppe |
| contents | Let $\mathbb Q_{ε_i}^{n_i}$ denote the simply connected space form of dimension $n_i\ge 2$ and constant sectional curvature $ε_i$. We prove that any connected isoparametric hypersurface of $\mathbb Q_{ε_1}^{n_1}\times\mathbb Q_{ε_2}^{n_2}$ has constant angle function. We then use this property to classify the isoparametric and homogeneous hypersurfaces of $\mathbb Q_{ε_1}^{n_1}\times\mathbb Q_{ε_2}^{n_2}$, $|ε_1|+|ε_2|\ne 0$, that satisfy a one-point condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isoparametric Hypersurfaces in Products of Simply Connected Space Forms de Lima, Ronaldo F. Pipoli, Giuseppe Differential Geometry 53A10 (primary), 53B25, 53C30 (secondary). 53A10 (primary), 53B25, 53C30 (secondary). 53A10 (primary), 53B25, 53C30 (secondary) Let $\mathbb Q_{ε_i}^{n_i}$ denote the simply connected space form of dimension $n_i\ge 2$ and constant sectional curvature $ε_i$. We prove that any connected isoparametric hypersurface of $\mathbb Q_{ε_1}^{n_1}\times\mathbb Q_{ε_2}^{n_2}$ has constant angle function. We then use this property to classify the isoparametric and homogeneous hypersurfaces of $\mathbb Q_{ε_1}^{n_1}\times\mathbb Q_{ε_2}^{n_2}$, $|ε_1|+|ε_2|\ne 0$, that satisfy a one-point condition. |
| title | Isoparametric Hypersurfaces in Products of Simply Connected Space Forms |
| topic | Differential Geometry 53A10 (primary), 53B25, 53C30 (secondary). 53A10 (primary), 53B25, 53C30 (secondary). 53A10 (primary), 53B25, 53C30 (secondary) |
| url | https://arxiv.org/abs/2511.12527 |