Cohomogeneity one actions on noncompact symmetric spaces of rank one

2005/05/24 by Jurgen Berndt, Berndt, Jurgen, Hiroshi Tamaru +1 · 2 citations
Mathematics · #53C35 #57S20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C35 #msc:57S20

paper · pdf · doi:10.48550/arxiv.math/0505490

13 pages

arxiv created 2005/05/24 · arxiv updated 2009/12/01

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 of dimension greater than two. For the quaternionic hyperbolic spaces of dimension greater than two 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.

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