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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: May 12, 2000
MathSciNet review: 1650061
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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.


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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: http://dx.doi.org/10.1090/S0002-9947-00-02439-9
PII: S 0002-9947(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