Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds
type: Item
instance of: scholarly article
title: Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds
zbMATH Open document ID: 0871.53048
DOI: 10.2307/2118566
author: Nadine Kowalsky
published in: Annals of Mathematics. Second Series
publication date: 1997-09-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 22E05
zbMATH DE Number: 986828
zbMATH Keywords: algebraic groups
zbMATH Keywords: Lorentzian manifold
zbMATH Keywords: stabilizers
reviewed by: Marcus Kriele
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118566
OpenAlex ID: W2331862326
description: scientific article; zbMATH DE number 986828