The half-space model of pseudo-hyperbolic space
| Autor: | Seppi, Andrea, Trebeschi, Enrico |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Developments in Lorentzian Geometry, Springer Proceedings in Mathematics and Statistics, 285-313, 2022 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages, 6 figures. Added Lemma 6.2 and additional details in the proofs of Propositions 2.5 and 5.1; other minor improvements and corrections |
| Databáze: | arXiv |
| Externí odkaz: |
|