Dynamical properties of the space of Lorentzian metrics
| dc.creator | Mounoud, Pierre | |
| dc.date | 2001-10-08 | |
| dc.date | 2003-01-17 | |
| dc.date.accessioned | 2026-07-07T04:43:42Z | |
| dc.date.available | 2026-07-07T04:43:42Z | |
| dc.description | We study the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. In particular, we prove that nonproperness entails the presence of lightlike geodesic foliations of codimension 1. On the 2-torus, we prove that a metric with constant curvature along one of its lightlike foliation is actually flat. This allows us to show that the restriction of the action to the set of non-flat metrics is proper and that on the set of flat metrics of volume 1 the action is ergodic. Finally, we show that, contrarily to the Riemannian case, the space of metrics without isometries is not always open. | |
| dc.description | 19 pages, Latex file, new introduction, to be published in Commentarii Mathematici Helvetici | |
| dc.identifier | https://arxiv.org/abs/math/0110082 | |
| dc.identifier | http://arxiv.org/abs/math/0110082 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62342 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58D17, (53C50, 53C12) | |
| dc.title | Dynamical properties of the space of Lorentzian metrics | |
| dc.type | text |