Hilbert metrics and Minkowski norms
| dc.creator | Foertsch, Thomas | |
| dc.creator | Karlsson, Anders | |
| dc.date | 2004-07-12 | |
| dc.date.accessioned | 2026-07-07T05:10:13Z | |
| dc.date.available | 2026-07-07T05:10:13Z | |
| dc.description | It is shown that the Hilbert geometry $(D,h_D)$ associated to a bounded convex domain $D\subset \mathbb{E}^n$ is isometric to a normed vector space $(V,||\cdot ||)$ if and only if $D$ is an open $n$-simplex. One further result on the asymptotic geometry of Hilbert's metric is obtained with corollaries for the behavior of geodesics. Finally we prove that every geodesic ray in a Hilbert geometry converges to a point of the boundary. | |
| dc.description | 11 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0407197 | |
| dc.identifier | http://arxiv.org/abs/math/0407197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71858 | |
| dc.subject | Metric Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 51Kxx, 53C60 | |
| dc.title | Hilbert metrics and Minkowski norms | |
| dc.type | text |