Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T15:55:27.530Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on Lorentz symmetric spaces

Published online by Cambridge University Press:  15 October 2004

Abdelghani Zeghib
Abdelghani Zeghib
Affiliation:
CNRS, UMPA, École Normale Supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, Francezeghib@umpa.ens-lyon.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider homogeneous Lorentz spaces of dimension at least 3. We prove that if such a space has ‘big’ isotropy (that is, a non-precompact and irreducible isotropy group), then this space must have constant sectional curvature. As a corollary, we obtain a new direct proof of the fact that irreducible Lorentz symmetric spaces have constant curvature, which was known via (algebraic) classification.

Keywords

Lorentz symmetricgeodesic hypersurfacenon-compact isotropy53B3022F30
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1675 - 1678
Copyright
Foundation Compositio Mathematica 2004