Finiteness theorems for equifocal hypersurfaces

TL;DR

This paper establishes finiteness results for the number of diffeomorphism types of equifocal hypersurfaces in symmetric spaces, with specific conditions relaxed in rank one cases.

Contribution

It proves a finiteness theorem for curvature-adapted equifocal hypersurfaces and extends results to rank one symmetric spaces without the curvature-adapted condition.

Findings

Finiteness of diffeomorphism types in symmetric spaces.

Relaxation of curvature-adapted condition in rank one spaces.

Extension of finiteness results to broader classes of hypersurfaces.

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.