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- Title
Dynamical properties of the space of Lorentzian metrics.
- Authors
Pierre Mounoud
- Abstract
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.
- Subjects
DIFFEOMORPHISMS; LORENTZ groups; G-spaces; METRIC spaces
- Publication
Commentarii Mathematici Helvetici, 2003, Vol 78, Issue 3, p463
- ISSN
0010-2571
- Publication type
Article
- DOI
10.1007/s00014-003-0767-8