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Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds. (English) Zbl 0871.53048

The author classifies those noncompact simple \(\mathbb{R}\)-algebraic groups \(G\) which act non-properly on a Lorentzian manifold \(M\) and preserve its metric. The main achievement over earlier work by other authors is that in the present paper \(M\) may be noncompact. The author proves that \(G\) must be locally isomorphic to \(\text{SL}(2,\mathbb{R})\) if all \(G\)-stabilizers are discrete. If \(G\) has arbitrary stabilizers, \(G\) can also be locally isomorphic to \(\text{SO}(n,1)\) or \(\text{SO}(n,2)\) for some \(n\). Part of her results can be generalized to pseudo-Riemannian manifolds.
Reviewer: M.Kriele (Berlin)

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
22E05 Local Lie groups
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