Showing papers by "Jurgen Berndt published in 2007"
TL;DR: In this article, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers were classified up to orbit equivalence and partial results were obtained.
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 CH", n ≥ 3. For the quaternionic hyperbolic spaces MH n , 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 Elie Cartan.
88 citations
01 Oct 2007
TL;DR: In this article, the authors classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane and show that all of them are open parts of homogeneous ones.
Abstract: We classify real hypersurfaces with constant principal curvatures in the complex hyperbolic plane. It follows from this classification that all of them are open parts of homogeneous ones. © 2007 American Mathematical Society.
31 citations