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Conformal actions of ${\mathfrak{sl}_n(\mathbb{R} )}$ and ${\hbox{SL}_n(\mathbb{R} )\ltimes\mathbb{R} ^n}$ on Lorentz manifolds


Authors: Scot Adams and Garrett Stuck
Journal: Trans. Amer. Math. Soc. 352 (2000), 3913-3936
MSC (1991): Primary 53C50, 54H15
DOI: https://doi.org/10.1090/S0002-9947-00-02439-9
Published electronically: May 12, 2000
MathSciNet review: 1650061
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Abstract | References | Similar Articles | Additional Information

Abstract:

We prove that, for $n\ge3$, a locally faithful action of ${\hbox{SL}_n(\mathbb{R} )\ltimes\mathbb{R} ^n}$ or of $\hbox{SL}_n({\mathbb R})$ by conformal transformations of a connected Lorentz manifold must be a proper action.


References [Enhancements On Off] (What's this?)

  • [A99] S. Adams. Induction of geometric actions. preprint, 1999.
  • [AS95] S. Adams and G. Stuck.
    The isometry group of a compact Lorentz manifold, I.
    Invent. Math. 129 (1997), no. 2, 239-261. MR 98i:53092
  • [AS97] S. Adams and G. Stuck.
    Isometric actions of ${\hbox{SL}_n({\mathbb R})\ltimes{\mathbb R}^n}$ on Lorentz manifolds.
    preprint, 1997.
  • [Helg78] S. Helgason.
    Differential Geometry, Lie Groups and Symmetric Spaces.
    Academic Press, 1978. MR 80k:53081
  • [KN63] S. Kobayashi and K. Nomizu.
    Foundations of Differential Geometry, Volume I.
    Interscience Publishers, New York, 1963.MR 97c:53001
  • [Kow96] N. Kowalsky.
    Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds.
    Ann. of Math. (2) 144 (1996), no. 3, 611-640. MR 98g:57059
  • [Thur74] W. Thurston.
    A generalization of the Reeb Stability Theorem.
    Topology 13 (1974), 347-352. MR 58:8558
  • [Var74] V. S. Varadarajan.
    Lie Groups, Lie Algebras, and Their Representations.
    Springer-Verlag, New York, 1974. MR 51:13113
  • [Gro88] M. Gromov.
    Rigid transformation groups.
    In: Géometrie différentielle, Travaux en cours, 33,
    Hermann, Paris, 1988. MR 90d:58173
  • [Zeg95] A. Zeghib.
    The identity component of the isometry group of a compact Lorentz manifold. Duke Math. J. 92 (1998), no. 2, 321-333. MR 98m:53091

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Additional Information

Scot Adams
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Garrett Stuck
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742

DOI: https://doi.org/10.1090/S0002-9947-00-02439-9
Keywords: Lorentz manifolds, isometries, transformation groups
Received by editor(s): March 24, 1998
Received by editor(s) in revised form: August 24, 1998
Published electronically: May 12, 2000
Additional Notes: The first author was supported in part by NSF grant DMS-9703480.
Article copyright: © Copyright 2000 American Mathematical Society

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