GEODESICS IN MARGULIS SPACETIMES

William M. Goldman (1) , François Labourie (2)

1 Department of Mathematics [College Park]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Let M3 be a Margulis spacetime whose associated complete hyperbolic surface Σ2 has compact convex core. Gen- eralizing the correspondence between closed geodesics on M3 and closed geodesics on Σ2, we establish an orbit equivalence between recurrent spacelike geodesics on M3 and recurrent geodesics on Σ2. In contrast, no timelike geodesic recurs in neither forward nor backwards time.

Domaines: Géométrie différentielle [math.DG]

William M. Goldman, François Labourie. GEODESICS IN MARGULIS SPACETIMES. Ergodic Theory and Dynamical Systems, 2011, ⟨10.1017/S0143385711000678⟩. ⟨hal-00627915⟩