Actions of noncompact semisimple groups on Lorentz manifolds

Mohamed Deffaf (1) , Karin Melnick (2) , Abdelghani Zeghib (3)

1 LATN - Laboratoire d'algèbre et de théorie des nombres
2 University of Chicago
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The above title is the same, but with "semisimple" instead of "simple," as that of a notice by N. Kowalsky. There, she announced many theorems on the subject of actions of simple Lie groups preserving a Lorentz structure. Unfortunately, she published proofs for essentially only half of the announced results before her premature death. Here, using a different, geometric approach, we generalize her results to the semisimple case, and give proofs of all her announced results.

Mots clés: semi-simple Lie groups; Lorentz manifolds; non proper actions; warped product

Domaines: Systèmes dynamiques [math.DS]; Géométrie différentielle [math.DG]

Mohamed Deffaf, Karin Melnick, Abdelghani Zeghib. Actions of noncompact semisimple groups on Lorentz manifolds. 2006. ⟨hal-00016628v2⟩