Finiteness theorems for equifocal hypersurfaces

2012/01/10 by Jianquan Ge, Chao Qian, Ge, Jianquan +3
Mathematics · #53C20 #53C40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG #msc:53C20 #msc:53C40

paper · pdf · doi:10.48550/arxiv.1201.2051

15 pages

arxiv created 2012/01/10 · openalex publication_date 2012/01/10 · arxiv updated 2012/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric space is of rank one.

Related

• Equifocal hypersurfaces in symmetric spaces of compact type and backward mean curvature flows
• On equifocal submanifolds with non-flat section in symmetric spaces of rank two
• A classification theorem of nondegenerate equiaffine symmetric hypersurfaces
• A total curvature estimate of closed hypersurfaces in non-positively curved symmetric spaces
• A construction of curvature-adapted hypersurfaces in the product of symmetric spaces