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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Length spectrum in rank one symmetric space is not arithmetic


Author: Inkang Kim
Journal: Proc. Amer. Math. Soc. 134 (2006), 3691-3696
MSC (2000): Primary 58D19, 53C23
Published electronically: May 31, 2006
MathSciNet review: 2240684
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Abstract: In this paper we show that a nonelementary nonparabolic group in a real semisimple Lie group of rank one has the property that the set of translation lengths of hyperbolic elements is not contained in any discrete subgroup of $ {\mathbb{R}}$.


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Additional Information

Inkang Kim
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Email: inkang@math.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08373-0
PII: S 0002-9939(06)08373-0
Received by editor(s): October 13, 2004
Received by editor(s) in revised form: June 16, 2005
Published electronically: May 31, 2006
Additional Notes: This work was partially supported by KOSEF Grant (R01-2005-000-10625-0(2005)).
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2006 American Mathematical Society