Canonical extension of submanifolds and foliations in noncompact symmetric spaces

2014/11/06 by Miguel Domínguez-Vázquez, Miguel Dominguez-Vazquez, Dominguez-Vazquez, Miguel
Mathematics · Physics and Astronomy · #53C12 (Secondary) #53C35 #53C42 (Primary) #57S20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C12 #msc:53C35 #msc:53C42 #msc:57S20

paper · pdf · doi:10.48550/arxiv.1411.1683

9 pages

arxiv created 2014/11/06 · openalex publication_date 2014/11/06 · arxiv updated 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a method to extend submanifolds, singular Riemannian foliations and isometric actions from a boundary component of a noncompact symmetric space to the whole space. This extension method preserves minimal submanifolds, isoparametric foliations and polar actions, among other properties. One of the several applications yields the first examples of inhomogeneous isoparametric hypersurfaces in noncompact symmetric spaces of rank at least two.

Related

• Submanifold geometry in symmetric spaces of noncompact type
• Homogeneous codimension-one foliations on reducible symmetric spaces of noncompact type
• Codimension two polar homogeneous foliations on symmetric spaces of noncompact type
• A class of complete embedded minimal submanifolds in noncompact symmetric spaces
• The classifications of certain kind of isoparametric submanifolds in non-compact symmetric spaces