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.