Fundamental Domains in Lorentzian Geometry
| dc.creator | Pratoussevitch, Anna | |
| dc.date | 2003-08-28 | |
| dc.date | 2004-11-02 | |
| dc.date.accessioned | 2026-07-07T13:15:08Z | |
| dc.date.available | 2026-07-07T13:15:08Z | |
| dc.description | We consider discrete subgroups Gamma of the simply connected Lie group SU~(1,1), the universal cover of SU(1,1), of finite level, i.e. the subgroup intersects the centre of SU~(1,1) in a subgroup of finite index, this index is called the level of the group. The Killing form induces a Lorentzian metric of constant curvature on the Lie group SU~(1,1). The discrete subgroup Gamma acts on SU~(1,1) by left translations. We describe the Lorentz space form SU~(1,1)/Gamma by constructing a fundamental domain F for Gamma. We want F to be a polyhedron with totally geodesic faces. We construct such F for all Gamma satisfying the following condition: The image of Gamma in PSU(1,1) has a fixed point u in the unit disk of order larger than the index of Gamma. The construction depends on the group Gamma and on the orbit Gamma(u) of the fixed point u. | |
| dc.description | 16 pages with 5 figures; typos corrected; introduction completed | |
| dc.identifier | https://arxiv.org/abs/math/0308279 | |
| dc.identifier | http://arxiv.org/abs/math/0308279 | |
| dc.identifier | Geom. Dedicata 126 (2007), 155-175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230388 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C50 (Primary); 14J17, 32S25, 51M20, 52B10 (Secondary) | |
| dc.title | Fundamental Domains in Lorentzian Geometry | |
| dc.type | text |