Let H be a closed, noncompact subgroup of a simple Lie group G, such that G/H admits an invariant Lorentz metric. We show that if G = SO(2, n), with n ≥ 3, then the identity component H of H is conjugate to SO(1, n). Also, if G = SO(1, n), with n ≥ 3, then H is conjugate to SO(1, n− 1).

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple identity component, 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...