
Journal of Lie Theory 30 (2020), No. 2, 565586 Copyright Heldermann Verlag 2020 Local and Global Rigidity for Isometric Actions of Simple Lie Groups on PseudoRiemannian Manifolds Raul QuirogaBarranco Centro de Investigación en Matemáticas, Guanajuato 36023, Mexico quiroga@cimat.mx Let M be a finite volume analytic pseudoRiemannian manifold that admits an isometric Gaction with a dense orbit, where G is a connected noncompact simple Lie group. For lowdimensional M, i.e. dim(M) < 2 dim(G), when the normal bundle to the Gorbits is nonintegrable and for suitable conditions, we prove that M has a Ginvariant metric which is locally isometric to a Lie group with a biinvariant metric (local rigidity theorem). The latter does not require $M$ to be complete as in previous works. We also prove a general result showing that M is, up to a finite covering, of the form H/Γ (Γ a lattice in the group H) when we assume that M is complete (global rigidity theorem). For both the local and the global rigidity theorems we provide cases that imply the rigidity of Gactions for G given by SO_{0}(p,q), G_{2(2)} or a noncompact simple Lie group of type F_{4} over R. We also survey the techniques and results related to this work. Keywords: PseudoRiemannian manifolds, exceptional Lie groups, rigidity results. MSC: 53C50, 53C24, 20G41, 57S20. [ Fulltextpdf (178 KB)] for subscribers only. 