NDLI: Géométries Lorentziennes de dimension 3 : classification et complétude

Content Provider	Springer Nature Link
Author	Zeghib, Abdelghani Dumitrescu, Sorin
Copyright Year	2010
Abstract	We classify three-dimensional Lorentz homogeneous spaces G/I having a compact manifold locally modeled on them. We prove a completeness result: any compact locally homogeneous Lorentz threefold M is isometric to a quotient of a Lorentz homogeneous space G/I by a discrete subgroup Γ of G acting properly and freely on G/I. Moreover, if I is noncompact, G/I is isometric to a Lie group L endowed with a left invariant Lorentz metric, where L is isomorphic to one of the following Lie groups: $${\bf R}^3, \widetilde{SL(2, {\bf R})}, He\,is \,{\rm or}\, SOL.$$ If L is not $${\widetilde{SL(2, {\bf R})}}$$ , then M admits a finite cover which is a quotient of L by a lattice.Nous classifions les géométries lorentziennes de dimension trois qui admettent des réalisations compactes. Nous démontrons un résultat de complétude : toute variété lorentzienne localement homogène compacte de dimension trois est isométrique au quotient (à gauche) d’un espace homogène lorentzien G/I de dimension trois par un sous-groupe discret Γ de G agissant proprement et librement. Si, de plus, le groupe d’isotropie locale de la métrique lorentzienne est supposé non compact, le revêtement universel de la variété est isométrique à un groupe de Lie L muni d’une métrique lorentzienne invariante par translation à gauche et L est isomorphe à l’un des groupes suivants : $${{\bf R}^3, \widetilde{SL(2, {\bf R})}, He\,is}$$ ou SOL. Si L n’est pas $${\widetilde{SL(2, {\bf R})}}$$ , alors la variété admet un revêtement fini qui est isométrique à un quotient de L par un réseau.
Ending Page	273
Page Count	31
Starting Page	243
File Format	PDF
ISSN	00465755
e-ISSN	15729168
Journal	Geometriae Dedicata
Issue Number	1
Volume Number	149
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-03-05
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Lorentz metrics, indefinite metrics Locally homogenous Lorentz manifolds Transitive Killing Lie algebras Geodesics Lorentz manifolds, manifolds with indefinite metrics Completeness of (G, X)-structures
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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