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Zbl 0951.53047
Salein, Fran{ç}ois
Variétés anti-de Sitter de dimension 3 exotiques. (Exotic 3-dimension anti-de Sitter manifolds). (French)
[J] Ann. Inst. Fourier 50, No.1, 257-284 (2000). ISSN 0373-0956; ISSN 1777-5310/e

{\it R. S. Kulkarni} and {\it F. Raymond} [J. Differ. Geom. 21, 231-268 (1985; Zbl 0563.57004)] gave the first examples of compact anti-de Sitter manifolds. Their examples are quotients of anti-de Sitter space by discrete groups of the form $\text{graph}(\rho)$, where $\rho\colon \Gamma\rightarrow\widetilde{\text{PSL}(2,\Bbb R)}$ is a homomorphism taking values in a compact subgroup of $\widetilde{\text{PSL}(2,\Bbb R)}$, and $\Gamma\subset\widetilde{\text{PSL}(2,\Bbb R)}$ is a discrete group. The goal of this paper is to give new examples of homomorphisms $\rho$ which generate exotic anti-de Sitter manifolds, that is, the homomorphisms $\rho$ are not continuous deformations of the trivial one.
[Pascual Lucas Saorín (Murcia)]

MSC 2000:: *53C50 Lorentz manifolds, manifolds with indefinite metrics
57S30 Discontinuous groups of transformations
53C30 Homogeneous manifolds
58H15 Global deformations of structures on manifolds
22E40 Discrete subgroups of Lie groups

Keywords: Lorentzian geometry; locally homogeneous manifold; discontinuous group of transformations; discrete group

Citations: Zbl 0563.57004

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