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Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces

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

preprint2020arXivOpen access
Jose Carlos Diaz-RamosMiguel Dominguez-VazquezAlberto Rodriguez-Vazquez
math.DG
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Jose Carlos Diaz-RamosMiguel Dominguez-VazquezAlberto Rodriguez-Vazquez

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