4 papers
On Lorentz dynamics : From group actions to warped products via homogeneous spaces
Abdelouahab Arouche, Mohamed Deffaf, Abdelghani Zeghib
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…
Dynamics on the space of harmonic functions and the foliated Liouville problem
R. Feres, A. Zeghib
We study here the action of subgroups of PSL(2,R) on the space of harmonic functions on the unit disc bounded by a common constant, as well as the relationship this action has with…
Leafwise Holomorphic Functions
R. Feres, A. Zeghib
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to…
Isometry groups and geodesic foliations of Lorentz manifolds. Part I: Foundations of Lorentz dynamics
Abdelghani Zeghib
This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present p…