Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One

  title={Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One},
  author={J{\"u}rgen Berndt and Hiroshi Tamaru},
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 CH, n ≥ 3. For the quaternionic hyperbolic spaces HH, n ≥ 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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