On equifocal submanifolds with non-flat section in symmetric spaces of rank two

TL;DR

This paper proves the non-existence of equifocal submanifolds with non-flat sections in certain symmetric spaces of rank two, and discusses properties of such sections in other similar spaces.

Contribution

It establishes a non-existence result for equifocal submanifolds with non-flat sections in specific symmetric spaces of rank two.

Findings

No such submanifolds exist in four irreducible simply connected symmetric spaces of compact type and rank two.

Provides insights into the sections of equifocal submanifolds with non-flat sections in other symmetric spaces.

Enhances understanding of the geometric structure of equifocal submanifolds in symmetric spaces.

Abstract

In this paper, we show that there exists no equifocal submanifold with non-flat section in four irreducible simply connected symmetric spaces of compact type and rank two. Also, we show a fact for the sections of equifocal submanifolds with non-flat section in other irreducible simply connected symmetric spaces of compact type and rank two.