The classification work Isoparametric hypersurfaces with four principal curvatures, and
Isoparametric hypersurfaces with four principal curvatures, II, left unsettled only those …

We prove that an isoparametric hypersurface with four principal curvatures and multiplicity
pair $(7, 8) $ is either the one constructed by Ozeki and Takeuchi, or one of the two …

The authors have been supported by projects MTM2016-75897-P (AEI/FEDER, UE),
EM2014/009, GRC2013-045 and MTM2013-41335-P with FEDER funds (Spain). The …

We provide an explicit classification of the following four families of surfaces in any
homogeneous 3-manifold with 4-dimensional isometry group: isoparametric surfaces …

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 …

We will show how isoparametric submanifolds and polar actions on round spheres lead to
polar foliations and polar actions on compact symmetric spaces and compact Riemannian …

We conclude the classification of isoparametric (or equivalently, polar) foliations of complex
and quaternionic projective spaces. This is done by investigating the projections of certain …

We classify the isoparametric hypersurfaces and the homogeneous hypersurfaces of
$\mathbb H^ n\times\mathbb R $ and $\mathbb S^ n\times\mathbb R $, $ n\ge 2$, by …

In this survey article we provide an introduction to submanifold geometry in symmetric
spaces of noncompact type. We focus on the construction of examples and the classification …

A hypersurface of a Riemannian manifold is called homogeneous if it is an orbit of an
isometric action on the ambient manifold. Homogeneous hypersurfaces have remarkable …