Kowalsky, Nadine Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds. (English) Zbl 0871.53048 Ann. Math. (2) 144, No. 3, 611-640 (1996). 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) Cited in 2 ReviewsCited in 17 Documents MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 22E05 Local Lie groups Keywords:algebraic groups; Lorentzian manifold; stabilizers × Cite Format Result Cite Review PDF Full Text: DOI