Cohomogeneity one actions on symmetric spaces of noncompact type

2010/06/10 by Jürgen Berndt, Berndt, Jurgen, Hiroshi Tamaru +1 · 1 citation
Mathematics · #53C35 (Primary) 57S20 (Secondary) #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1006.1980

openalex publication_date 2010/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As a consequence, we find many new examples of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type. We apply our conceptual approach to derive explicit classifications of cohomogeneity one actions on some symmetric spaces.

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• On Hopf hypersurfaces of the complex hyperbolic quadric with constant principal curvatures

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