| Abstract: | We study the mechanisms of the non properness of the action ofthe group of diffeomorphisms on the space of Lorentzian metricsof a compact manifold.In particular, we prove that nonproperness entails the presence oflightlike geodesic foliations of codimension 1.On the 2-torus, we prove that a metric with constant curvaturealong one of its lightlike foliation is actually flat. Thisallows 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, thespace of metrics without isometries is not always open. |
