If a topological group G acts on a topological space M, then we say that the action is orbit nonproper provided that, for some m0 ∈ M, the orbit map g → gm0 : G → M is nonproper. In this paper we characterize the connected, simply connected Lie groups that admit a locally free, orbit nonproper action by isometrics of a connected Lorentz manifold. We also consider a number of variants on this question.
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The author was supported in part by NSF grant DMS-9703480.
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