On Lorentz dynamics : From group actions to warped products via homogeneous spaces

Abdelouahab Arouche (1) , Mohamed Deffaf (1) , Abdelghani Zeghib (2)

1 LATN-USTHB - Laboratoire d'algèbre et théorie des nombres
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.

Mots clés: lorentz manifold; noncompact action; semisimple Lie group; warped product; homogeneous space

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

Abdelouahab Arouche, Mohamed Deffaf, Abdelghani Zeghib. On Lorentz dynamics : From group actions to warped products via homogeneous spaces. 2004. ⟨hal-00003480⟩