Title: Extension of submanifolds in symmetric spaces of noncompact type
Abstract: A maximal flat in a symmetric space of noncompact
type is a Euclidean space embedded in a totally geodesic way. In this
talk I will present a simple method that allows to enlarge
submanifolds of a maximal flat to the whole ambient symmetric space,
in such a way that the codimension, the mean curvature, and other
geometric properties are preserved. As an application, I will explain
how one can construct the first examples of inhomogeneous
isoparametric hypersurfaces in each symmetric space of noncompact type
and rank higher than two. This is based on a joint work with Victor
Sanmartin-López.