This second edition explores recent progress in the submanifold geometry of space forms,
including new methods based on the holonomy of the normal connection. It contains five …

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 …

These are the notes for a series of lectures at the Institute of Geometry and Topology of the
University of Stuttgart, Germany, in July 13-15, 2022. We assume basic knowledge of …

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 give a geometric characterization of certain hypersurfaces of cohomogeneity one in the
complex projective and hyperbolic planes. We also obtain some partial classifications of …

In this article we classify totally geodesic submanifolds in arbitrary products of rank one
symmetric spaces. Furthermore, we give infinitely many examples of irreducible totally …

We develop a new structural result for cohomogeneity one actions on (not necessarily
irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to …

A hypersurface in a Riemannian manifold is called isoparametric if it and its nearby
equidistant hypersurfaces have constant mean curvature. These geometric objects, as well …

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in
complex projective and hyperbolic planes, and we classify them. It turns out that each such …

Any homogeneous expanding Ricci soliton is known to be isometric to a Lie subgroup of the
solvable part of the Iwasawa decomposition associated with a symmetric space of non …