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On the symmetries of rigid geometric structures. (Sur les symétries des structures géométriques rigides.) (French) Zbl 1227.53019
Actes de Séminaire de Théorie Spectrale et Géométrie. Année 2009–2010. St. Martin d’Hères: Université de Grenoble I, Institut Fourier. Séminaire de Théorie Spectrale et Géométrie 28, 29-49 (2010).
The author presents classification results of Lorentzian spaces of dimension three. The main theorems concern the classification of compact connected Lorentzian spaces which are locally modeled on a Lorentzian geometry $$(G,G/I)$$, which they derive either from the Minkowski or the de Sitter or the Lorentz-Heisenberg geometry. In particular, a compact locally homogeneous Lorentzian space of dimension three is isometric to a quotient space obtained under the proper action of a discrete subgroup $$\Gamma \subset G$$ on $$G/I$$. Another result is related to the sectional curvature of some compact Lorentzian spaces.
This is a clear summary of results on this topic obtained over several years by many authors, and it contains useful references.
For the entire collection see [Zbl 1213.35007].
##### MSC:
 53B21 Methods of local Riemannian geometry 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 53C56 Other complex differential geometry 53A55 Differential invariants (local theory), geometric objects
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