Group actions on Lorentz spaces, mathematical aspects: a survey

Abstract

From a purely mathematical viewpoint, one can say that most recent works in Lorentz geometry, concern group actions on Lorentz manifolds. For instance, the three major themes: space form problem of Lorentz homogeneous spacetimes, the completeness problem, and the classification problem of large isometry groups of Lorentz manifolds, all deal with group actions. However, in the first two cases, actions are “zen” (e.g., proper), and in the last, the action is violent (i.e., with strong dynamics). We will survey recent progress in these themes, but we will focus attention essentially on the last one, that is, on Lorentz dynamics