Dynamical properties of the space of Lorentzian metrics

• Autores: Pierre Mounoud
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 78, Nº 3, 2003, págs. 463-485
• Idioma: inglés
• DOI: 10.1007/s00014-003-0767-8
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• Resumen

  • 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.