Complete cohomogeneity one hypersurfaces of $\mathbb{H}^{n+1}$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910559542181888 |
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| author | Guimarães, Felippe Manfio, Fernando Olmos, Carlos E. |
| author_facet | Guimarães, Felippe Manfio, Fernando Olmos, Carlos E. |
| contents | We study isometric immersions $f: M^n \rightarrow \mathbb{H}^{n+1}$ into hyperbolic space of dimension $n+1$ of a complete Riemannian manifold of dimension $n$ on which a compact connected group of intrinsic isometries acts with principal orbits of codimension one. We provide a characterization if either $n \geq 3$ and $M^n$ is compact, or $n \geq 5$ and the connected components of the set where the sectional curvature is constant and equal to $-1$ are bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete cohomogeneity one hypersurfaces of $\mathbb{H}^{n+1}$ Guimarães, Felippe Manfio, Fernando Olmos, Carlos E. Differential Geometry 53C42, 53C40, 53C30 We study isometric immersions $f: M^n \rightarrow \mathbb{H}^{n+1}$ into hyperbolic space of dimension $n+1$ of a complete Riemannian manifold of dimension $n$ on which a compact connected group of intrinsic isometries acts with principal orbits of codimension one. We provide a characterization if either $n \geq 3$ and $M^n$ is compact, or $n \geq 5$ and the connected components of the set where the sectional curvature is constant and equal to $-1$ are bounded. |
| title | Complete cohomogeneity one hypersurfaces of $\mathbb{H}^{n+1}$ |
| topic | Differential Geometry 53C42, 53C40, 53C30 |
| url | https://arxiv.org/abs/2408.03802 |