Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds
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.
scientific article; zbMATH DE number 986828