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Cohomogeneity one actions on noncompact symmetric spaces of rank one


Authors: Jürgen Berndt and Hiroshi Tamaru
Journal: Trans. Amer. Math. Soc. 359 (2007), 3425-3438
MSC (2000): Primary 53C35; Secondary 57S20
DOI: https://doi.org/10.1090/S0002-9947-07-04305-X
Published electronically: January 26, 2007
MathSciNet review: 2299462
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Abstract: We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces $ \mathbb{C} H^n$, $ n \geq 3$. For the quaternionic hyperbolic spaces $ \mathbb{H} H^n$, $ n \geq 3$, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classification problem was essentially solved by Élie Cartan.


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Additional Information

Jürgen Berndt
Affiliation: Department of Mathematics, University College, Cork, Ireland
Email: j.berndt@ucc.ie

Hiroshi Tamaru
Affiliation: Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi- Hiroshima, 739-8526, Japan
Email: tamaru@math.sci.hiroshima-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-07-04305-X
Keywords: Symmetric spaces, hyperbolic spaces, cohomogeneity one actions, homogeneous hypersurfaces
Received by editor(s): July 12, 2005
Published electronically: January 26, 2007
Additional Notes: The second author was partially supported by Grant-in-Aid for Young Scientists (B) 14740049 and 17740039, The Ministry of Education, Culture, Sports, Science and Technology, Japan
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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