×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EuDML