On Lorentz dynamics: From group actions to warped products via homogeneous spaces
HTML articles powered by AMS MathViewer
- by A. Arouche, M. Deffaf and A. Zeghib PDF
- Trans. Amer. Math. Soc. 359 (2007), 1253-1263 Request permission
Abstract:
We show a geometric rigidity of isometric actions of non-compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.References
- Scot Adams, Dynamics of simple Lie groups on Lorentz manifolds, Geom. Dedicata 105 (2004), 1–12. MR 2057240, DOI 10.1023/B:GEOM.0000024726.35086.c4
- Scot Adams and Garrett Stuck, The isometry group of a compact Lorentz manifold. I, II, Invent. Math. 129 (1997), no. 2, 239–261, 263–287. MR 1465326, DOI 10.1007/s002220050163
- Charles Boubel and Abdelghani Zeghib, Isometric actions of Lie subgroups of the Moebius group, Nonlinearity 17 (2004), no. 5, 1677–1688. MR 2086144, DOI 10.1088/0951-7715/17/5/006
- Michael Gromov, Rigid transformations groups, Géométrie différentielle (Paris, 1986) Travaux en Cours, vol. 33, Hermann, Paris, 1988, pp. 65–139. MR 955852
- Sönke Hiepko, Eine innere Kennzeichnung der verzerrten Produkte, Math. Ann. 241 (1979), no. 3, 209–215 (German). MR 535555, DOI 10.1007/BF01421206
- Nadine Kowalsky, Actions of non-compact simple groups of Lorentz manifolds, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 5, 595–599 (English, with English and French summaries). MR 1356560
- Nadine Kowalsky, Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds, Ann. of Math. (2) 144 (1996), no. 3, 611–640. MR 1426887, DOI 10.2307/2118566
- Ralf Ponge and Helmut Reckziegel, Twisted products in pseudo-Riemannian geometry, Geom. Dedicata 48 (1993), no. 1, 15–25. MR 1245571, DOI 10.1007/BF01265674
- Dave Witte, Homogeneous Lorentz manifolds with simple isometry group, Beiträge Algebra Geom. 42 (2001), no. 2, 451–461. MR 1865533
- Abdelghani Zeghib, Remarks on Lorentz symmetric spaces, Compos. Math. 140 (2004), no. 6, 1675–1678. MR 2098408, DOI 10.1112/S0010437X04000466
- Abdelghani Zeghib, Sur les espaces-temps homogènes, The Epstein birthday schrift, Geom. Topol. Monogr., vol. 1, Geom. Topol. Publ., Coventry, 1998, pp. 551–576 (French, with English summary). MR 1668344, DOI 10.2140/gtm.1998.1.551
- A. Zeghib, Isometry groups and geodesic foliations of Lorentz manifolds. II. Geometry of analytic Lorentz manifolds with large isometry groups, Geom. Funct. Anal. 9 (1999), no. 4, 823–854. MR 1719610, DOI 10.1007/s000390050103
- Robert J. Zimmer, On the automorphism group of a compact Lorentz manifold and other geometric manifolds, Invent. Math. 83 (1986), no. 3, 411–424. MR 827360, DOI 10.1007/BF01394415
Additional Information
- A. Arouche
- Affiliation: Faculté des Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El’Alia, Bab Ezzouar, Alger, Algeria
- Email: arouche@math.usthb.dz
- M. Deffaf
- Affiliation: Faculté des Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El’Alia, Bab Ezzouar, Alger, Algeria
- Email: deffaf1@yahoo.fr
- A. Zeghib
- Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364 Lyon cedex 07, France
- Email: Zeghib@umpa.ens-lyon.fr
- Received by editor(s): December 14, 2004
- Published electronically: October 17, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 1253-1263
- MSC (2000): Primary 53C50, 54H15
- DOI: https://doi.org/10.1090/S0002-9947-06-04279-6
- MathSciNet review: 2262849