A splitting theorem for equifocal submanifolds with non-flat section

TL;DR

This paper proves a splitting theorem for equifocal submanifolds with non-flat sections in symmetric spaces, showing their sections are isometric to spheres or real projective spaces, advancing understanding of their geometric structure.

Contribution

It introduces a splitting theorem for equifocal submanifolds with non-flat sections in symmetric spaces, classifying their sections as spheres or real projective spaces.

Findings

Sections are isometric to spheres or real projective spaces

Splitting theorem applies to simply connected symmetric spaces of compact type

Provides new classification results for equifocal submanifolds

Abstract

In this paper, I prove a splitting theorem for equifocal submanifolds with non-flat section in a simply connected symmetric space of compact type. Also, by using the splitting theorem, I prove that the sections of equifocal submanifolds with non-flat section in an irreducible simply connected symmetric space of compact type are isometric to a sphere or a real projective space.