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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cohomogeneity one actions on noncompact symmetric spaces of rank one
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by Jürgen Berndt and Hiroshi Tamaru PDF
Trans. Amer. Math. Soc. 359 (2007), 3425-3438 Request permission


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:
  • Hiroshi Tamaru
  • Affiliation: Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi- Hiroshima, 739-8526, Japan
  • MR Author ID: 645435
  • Email:
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 3425-3438
  • MSC (2000): Primary 53C35; Secondary 57S20
  • DOI:
  • MathSciNet review: 2299462