Miguel DomÍnguez Vázquez, Santiago de Compostela

Title: Homogeneous and inhomogeneous isoparametric hypersurfaces in quaternionic hyperbolic spaces

Abstract: In this talk I will report on a recent joint work with
J. Carlos Díaz-Ramos and Alberto Rodríguez-Vázquez where we
conclude the classification of cohomogeneity one actions on symmetric
spaces of rank one (up to orbit equivalence) by classifying such
actions on quaternionic hyperbolic spaces. As a consequence of our
approach, we find uncountably many examples of inhomogeneous
isoparametric families of hypersurfaces with constant principal
curvatures in quaternionic hyperbolic spaces. This contrasts with the
isoparametric theory in the other symmetric spaces of rank one.