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 C H n \mathbb C H^n , n ≥ 3 n \geq 3 . For the quaternionic hyperbolic spaces H H n \mathbb H H^n , n ≥ 3 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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