Isoparametric surfaces in homogeneous 3-manifolds

Abstract: A hypersurface of a Riemannian manifold is called isoparametric if it and its nearby equidistant hypersurfaces have constant mean curvature. Cartan proved that a hypersurface in a space of constant curvature is isoparametric if and only if it has constant principal curvatures. However, this characterization does not necessarily hold in spaces of nonconstant curvature. In this talk I will present a recent joint work with José Miguel Manzano (ICMAT-CSIC, Madrid) where we initiated the study of isoparametric surfaces and surfaces with constant principal curvatures in homogeneous 3-manifolds, obtaining their classification in the homogeneous 3-spaces with 4-dimensional isometry group.

Hosts: Quo-Shin Chi & Yanli Song