Metadata
Abstract
In this paper, we give a complete topological, as well as geometrical classification of closed -dimensional Lorentz manifolds admitting a noncompact isometry group.
References
[Amo79] Vector fields of a finite type G-structure, J. Differ. Geom., Volume 14 (1979) no. 1, pp. 1-6 | DOI | MR | Zbl
[AS97] The isometry group of a compact Lorentz manifold. I, II, Invent. Math., Volume 129 (1997) no. 2, p. 239-261, 263–287 | DOI | MR | Zbl
[BCD + 08] A primer on the Einstein universe, Recent developments in pseudo-Riemannian geometry (ESI Lectures in Mathematics and Physics), European Mathematical Society, 2008, pp. 179-229 | DOI | Zbl
[BM16] Extension maximale et classification des tores lorentziens munis d’un champ de Killing (2016) (https://arxiv.org/abs/1510.01253v2) | Zbl
[Car89] Autour de la conjecture de L. Markus sur les variétés affines, Invent. Math., Volume 95 (1989) no. 3, pp. 615-628 | DOI | MR | Zbl
[DG91] Lectures on transformations groups: geometry and dynamics, Surveys in Differential Geometry Vol. I: Proceedings of the conference on geometry and topology, held at Harvard University, (Cambridge, MA, 1990), American Mathematical Society, 1991, pp. 19-111 | DOI
[DM15] Quasihomogeneous three-dimensional real-analytic Lorentz metrics do not exist, Geom. Dedicata, Volume 179 (2015), pp. 229-253 | DOI | MR | Zbl
[DZ10] Géométries Lorentziennes de dimension 3: classification et complétude, Geom. Dedicata, Volume 149 (2010), pp. 243-273 | DOI | Zbl
[D’A88] Sometry groups of Lorentz manifolds, Invent. Math., Volume 92 (1988) no. 3, pp. 555-565 | MR
[FG83] Three-dimensional affine crystallographic groups, Adv. Math., Volume 47 (1983) no. 1, pp. 1-49 | DOI | MR | Zbl
[Fra02] Géométrie et dynamique lorentziennes conformes (2002) (Ph. D. Thesis)
[Fra18] Variations on Gromov’s open-dense orbit theorem, Bull. Soc. Math. Fr., Volume 146 (2018) no. 4, pp. 713-744 | DOI | MR | Zbl
[FZ02] Geometric lattice actions, entropy and fundamental groups, Comment. Math. Helv., Volume 77 (2002) no. 2, pp. 326-338 | DOI | MR | Zbl
[GK84] The fundamental group of a compact flat Lorentz space form is virtually polycyclic, J. Differ. Geom., Volume 19 (1984) no. 1, pp. 233-240 | DOI | MR | Zbl
[God91] Feuilletages. Études géométriques, Progress in Mathematics, Volume 98, Birkhäuser, 1991 | MR | Zbl
[Gro88] Rigid transformation groups, Géométrie Différentielle (Travaux en Cours) Volume 33, Hermann, 1988, pp. 65-141 | MR | Zbl
[Kli96] Complétude des variétés lorentziennes à courbure constante, Math. Ann., Volume 306 (1996) no. 2, pp. 353-370 | DOI | MR | Zbl
[KN63] Foundations of differential geometry I, Interscience Publishers, 1963
[KR85] -dimensional Lorentz space-forms and Seifert fiber spaces, J. Differ. Geom., Volume 21 (1985) no. 2, pp. 231-268 | DOI | MR | Zbl
[Mel11] A Frobenius theorem for Cartan geometries, with applications, Enseign. Math., Volume 57 (2011) no. 1-2, pp. 57-89 | DOI | MR | Zbl
[MS39] The group of isometries of a Riemannian manifold, Ann. Math., Volume 40 (1939) no. 2, pp. 400-416 | DOI | MR
[Nom53] On the group of affine transformations of an affinely connected manifold, Proc. Am. Math. Soc., Volume 4 (1953), pp. 816-823 | DOI | MR | Zbl
[Orl72] Seifert Manifolds, Lecture Notes in Mathematics, Volume 291, Springer, 1972 | MR | Zbl
[Péc16] On two theorems about local automorphisms of geometric structures, Ann. Inst. Fourier, Volume 66 (2016) no. 1, pp. 175-208 | DOI | Numdam | MR | Zbl
[Sal99] Variétés anti-de Sitter de dimension 3 (1999) (http://www.umpa.ens-lyon.fr/~zeghib/these.salein.pdf) (Ph. D. Thesis) | Zbl
[Sco83] The geometries of 3-manifolds, Bull. Lond. Math. Soc., Volume 15 (1983) no. 5, pp. 401-487 | DOI | MR | Zbl
[Sha97] Differential Geometry: Cartan’s generalization of Klein’s Erlangen Program, Graduate Texts in Mathematics, Volume 166, Springer, 1997 | MR | Zbl
[Tho14] Uniformisation des variétés pseudo-riemanniennes localement homogènes (2014) (Ph. D. Thesis)
[Zeg96] Killing fields in compact Lorentz 3-manifolds, J. Differ. Geom., Volume 43 (1996) no. 4, pp. 859-894 | DOI | MR | Zbl
[Zeg98] Sur les espaces-temps homogènes. [Homogeneous spacetimes], The Epstein birthday schrift (Geometry and Topology Monographs) Volume 1, Geometry and Topology Publications, 1998, pp. 551-576 | DOI | MR | Zbl
[Zeg99a] Geodesic foliations in Lorentz 3-manifolds, Comment. Math. Helv., Volume 74 (1999) no. 1, pp. 1-21 | DOI | MR | Zbl
[Zeg99b] Isometry groups and geodesic foliations of Lorentz manifolds. I. Foundations of Lorentz dynamics., Geom. Funct. Anal., Volume 9 (1999) no. 4, pp. 775-822 | DOI | MR
[Zeg99c] Isometry groups and geodesic foliations of Lorentz manifolds. II. Geometry of analytic Lorentz manifolds with large isometry group, Geom. Funct. Anal., Volume 9 (1999) no. 4, pp. 823-854 | DOI | MR | Zbl
[Zim86] On the automorphism group of a compact Lorentz manifold and other geometric manifolds, Invent. Math., Volume 83 (1986) no. 3, pp. 411-424 | DOI | MR | Zbl