Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one\n symmetric spaces

2020/05/19 by José Carlos Díaz-Ramos, Diaz-Ramos, Jose Carlos, Miguel Domínguez-Vázquez +3 · 3 citations
Mathematics · #53C35 (Primary) #53C40 (Secondary) #57S20 #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2005.09314

openalex publication_date 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We conclude the classification of cohomogeneity one actions on symmetric\nspaces of rank one by classifying cohomogeneity one actions on quaternionic\nhyperbolic spaces up to orbit equivalence. As a by-product of our proof, we\nproduce uncountably many examples of inhomogeneous isoparametric families of\nhypersurfaces with constant principal curvatures in quaternionic hyperbolic\nspaces.\n

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• On Hopf hypersurfaces of the complex hyperbolic quadric with constant principal curvatures
• Homogeneous hypersurfaces of the four-dimensional Thurston geometry \rm Sol₀⁴
• Classification of Certain Rational Isoparametric Functions on Damek-Ricci Spaces

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