Locally free actions on Lorentz manifolds

If a topological group G acts on a topological space M, then we say that the action is orbit nonproper provided that, for some ,the orbit map is nonproper. In this paper we characterize the connected, simply connected Lie groups that admit a locally free, orbit nonproper action by isometries of a connected Lorentz manifold. We also consider a number of variants on this question. Submitted: November 1998, Revised version: April 1999, Final version: April 2000.