Fundamental domains in Lorentzian geometry |
| |
Authors: | Anna Pratoussevitch |
| |
Institution: | 1.Mathematisches Institut,Universit?t Bonn,Bonn,Germany |
| |
Abstract: | We consider a discrete subgroup Γ of the simply connected Lie group of finite level, i.e. the subgroup intersects the centre of 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 . The discrete subgroup Γ acts on by left translations. We describe the Lorentz space form by constructing a fundamental domain F for Γ. We want F to be a polyhedron with totally geodesic faces. We construct such F for all Γ satisfying the following condition: The image of Γ in PSU(1,1) has a fixed point u in the unit disk of order larger than the index of Γ. The construction depends on the group Γ and on the orbit Γ(u) of the fixed point u.
|
| |
Keywords: | Lorentz space form Polyhedral fundamental domain Quasihomogeneous singularity Arnold singularity series |
本文献已被 SpringerLink 等数据库收录! |
|