Lorentz Dynamics on Closed 3-Manifolds

In this paper, we give a complete topological, as well as geometrical classification of closed 3-dimensional Lorentz manifolds admitting a noncompact isometry group

Conformal actions of nilpotent groups on pseudo-Riemannian manifolds

We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M supports a conformal action of a connected nilpotent group H, then the degree of nilpotence of H is at most 2p+1, assuming p <= q; further, if this maximal degree is attained, then M is conformally equivalent to the universal type-(p,q), compact, conformally flat space, up to finite covers. The proofs make use of the canonical Cartan geometry associated to a pseudo-Riemannian conformal structure.Comment: 41 pages, 3 figures. Article has been shortened from previous version, and several corrections have been made according to referees' suggestion

Formes normales pour les champs conformes pseudo-riemanniens

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is conformally flat. In either case, the vector field is locally conjugate to a normal form on a model space. For smooth metrics of general signature, we obtain the analogous result under the additional assumption that the differential of the flow at the fixed point is bounded.Comment: 49 pages, Minor modifications according to referee's comments. To appear in Bulletin de la SM