Length spectrum in rank one symmetric space is not arithmetic

Kim, Inkang

doi:10.1090/S0002-9939-06-08373-0

Length spectrum in rank one symmetric space is not arithmetic
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Proc. Amer. Math. Soc. 134 (2006), 3691-3696 Request permission

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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