Rob Milson - Realization of reflection quotients by singular metrics

The Killing-Hopf theorem states that a complete surface of constant curvature is the quotient of a simply connected space form by a group of orientation preserving isometries. I will discuss a generalization of this classical theorem that deals with quotients by reflection groups. The geometric setting for this generalization is furnished by a certain class of singular metric tensors such that the fixed points of the generating reflections correspond to the locus of the metric's singularity.