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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, [email protected]
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Abstract

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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