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Zbl 0897.53048
Salein, François
Anti-de Sitter manifolds of dimension 3. (Variétés anti-de Sitter de dimension 3.) (French)
[A] Séminaire de théorie spectrale et géométrie. Année 1996-1997. St. Martin D'Hères: Univ. de Grenoble I, Institut Fourier, Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 15, 37-42 (1997).

The aim of this paper is to give all anti-de Sitter manifolds of three dimensions which have a nontrivial Killing vector field. An anti-de Sitter manifold is a Lorentz manifold with constant curvature equal to $-1$, and the modelling Lie group is $\text {PSL}_2 (\bbfR)$. Because the only nontrivial Killing vector field on $\text {PSL}_2 (\bbfR)$ is generated by the subgroup with one parameter of $\text {PSL}_2 (\bbfR) \times \text {PSL}_2 (\bbfR)$, the study of three dimensional anti-de Sitter manifolds which admit a nontrivial Killing vector field is equivalent to finding all admissible representations in a subgroup of one parameter. For details of the proof the reader is reffered to {\it F. Salein} [C. R. Acad. Sci., Paris, Sér. I 324, 525-530 (1997)].
[S.Noaghi (Vulcan)]

MSC 2000:: *53C50 Lorentz manifolds, manifolds with indefinite metrics

Keywords: 3-dimensional anti-de Sitter manifold; Killing vector field

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