The half-space model of pseudo-hyperbolic space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866917813942222848 |
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| author | Seppi, Andrea Trebeschi, Enrico |
| author_facet | Seppi, Andrea Trebeschi, Enrico |
| contents | In this note we develop a half-space model for the pseudo-hyperbolic space $\mathbb{H}^{p,q}$, for any $p,q$ with $p\geq 1$. This half-space model embeds isometrically onto the complement of a degenerate totally geodesic hyperplane in $\mathbb{H}^{p,q}$. We describe the geodesics, the totally geodesic submanifolds, the horospheres, the isometry group in the half-space model, and we explain how to interpret the boundary at infinity in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_11122 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The half-space model of pseudo-hyperbolic space Seppi, Andrea Trebeschi, Enrico Differential Geometry Geometric Topology In this note we develop a half-space model for the pseudo-hyperbolic space $\mathbb{H}^{p,q}$, for any $p,q$ with $p\geq 1$. This half-space model embeds isometrically onto the complement of a degenerate totally geodesic hyperplane in $\mathbb{H}^{p,q}$. We describe the geodesics, the totally geodesic submanifolds, the horospheres, the isometry group in the half-space model, and we explain how to interpret the boundary at infinity in this setting. |
| title | The half-space model of pseudo-hyperbolic space |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2106.11122 |