Isometric actions of simple Lie groups on pseudoRiemannian manifolds
| dc.creator | Quiroga-Barranco, Raul | |
| dc.date | 2007-01-08 | |
| dc.date | 2007-03-13 | |
| dc.date.accessioned | 2026-07-07T07:51:22Z | |
| dc.date.available | 2026-07-07T07:51:22Z | |
| dc.description | Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m_0, n_0 are the dimensions of the maximal lightlike subspaces tangent to M and G, respectively, where G carries any bi-invariant metric, then we have n_0 \leq m_0. We study G-actions that satisfy the condition n_0 = m_0. With no rank restrictions on G, we prove that M has a finite covering \hat{M} to which the G-action lifts so that \hat{M} is G-equivariantly diffeomorphic to an action on a double coset K\backslash L/Γ, as considered in Zimmer's program, with G normal in L (Theorem A). If G has finite center and \rank_\R(G)\geq 2, then we prove that we can choose \hat{M} for which L is semisimple and Γis an irreducible lattice (Theorem B). We also prove that our condition n_0 = m_0 completely characterizes, up to a finite covering, such double coset G-actions (Theorem C). This describes a large family of double coset G-actions and provides a partial positive answer to the conjecture proposed in Zimmer's program. | |
| dc.description | 29 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0701185 | |
| dc.identifier | http://arxiv.org/abs/math/0701185 | |
| dc.identifier | Ann. of Math. (2) 164 (2006), no. 3, 941--969 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125489 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 53C24: 53C50 | |
| dc.title | Isometric actions of simple Lie groups on pseudoRiemannian manifolds | |
| dc.type | text |