Compact Lorentz manifolds with local symmetry

Abstract

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, as- pherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple identity com- ponent, then the local isometry orbits in M are roughly fibers of a fiber bundle. A corollary is that if M has an open, dense, locally homogeneous subset, then M is locally homogeneous.