English

Actions of noncompact semisimple groups on Lorentz manifolds

Dynamical Systems 2007-05-23 v3 Differential Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0601165,
  title  = {Actions of noncompact semisimple groups on Lorentz manifolds},
  author = {Mohamed Deffaf and Karin Melnick and Abdelghani Zeghib},
  journal= {arXiv preprint arXiv:math/0601165},
  year   = {2007}
}

Comments

25 pp, to appear in Geometric and Functional Analysis sharpened thm 1.9 to give global description of actions in all cases; added section 8 on structure of orbits of Riemannian type and how Riemannian and Lorentzian orbits meet around degenerate set; many minor corrections and improvements thanks to referee's comments

R2 v1 2026-07-22T17:29:40.350Z