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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
Posted:
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  .
References
- 1.
M. Babillot, Ergodic theory, Geometric rigidity and number theory conference at Isaac Newton Institute, July 2000.
- 2.
M. Cowling, A. Dooley, A. Korányi, F. Ricci, H-type groups and Iwasawa decompositions, Adv. Math. 87 (1991), no. 1, 1-41. MR 1102963 (92e:22017)
- 3.
M. Cowling, A. Dooley, A. Korányi, F. Ricci, An approach to symmetric spaces of rank one via groups of Heisenberg type, J. Geom. Anal. 8 (1998), no. 2, 199-237. MR 1705176 (2000m:53071)
- 4.
F. Dal'Bo, Topologie du feuilletage fortement stable, Ann. Inst. Fourier 50 (2000), no. 3, 981-993. MR 1779902 (2001i:37045)
- 5.
F. Dal'Bo, Remarques sur le spectre des longueurs d'une surface et comptages, Bol. Soc. Brasil. Mat. 30 (1999), no. 2, 199-221.MR 1703039 (2000i:53117)
- 6.
F. Dal'Bo and I. Kim, Marked length rigidity for symmetric spaces, Comment. Math. Helv. 77 (2002), no. 2, 399-407. MR 1915048 (2003g:53058)
- 7.
Inkang Kim, Marked length rigidity of rank one symmetric spaces and their product, Topology 40 (2001), no. 6, 1295-1323. MR 1867246 (2002m:53064)
- 8.
Inkang Kim, Rigidity on symmetric spaces, Topology 43 (2004), no. 2, 393-405. MR 2052969 (2005d:53067)
- 9.
Inkang Kim, Ergodic theory and rigidity on the symmetric space of noncompact type, Ergodic Theory Dynam. Systems 21 (2001), no. 1, 93-114. MR 1826662 (2002c:37034)
- 10.
Inkang Kim, Isospectral finiteness on hyperbolic 3-manifolds, Comm. Pure and Appl. Math. 59 (2006), no. 5, 617-625.
- 11.
G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, no. 78, Princeton Univ. Press, Princeton, NJ, 1973. MR 0385004 (52:5874)
- 12.
J-P. Otal, Sur la géometrie symplectique de l'espace des géodésiques d'une variété à courbure négative, Rev. Mat. Iberoamericana 8 (1992), no. 3, 441-456. MR 1202417 (94a:58077)
- 13.
Pansu, P., Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989), 1-60. MR 0979599 (90e:53058)
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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
Posted:
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
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