Homogeneity of proper complex equifocal submanifolds

TL;DR

This paper proves that irreducible proper complex equifocal submanifolds of codimension greater than one in non-compact symmetric spaces are homogeneous by analyzing their lifts to an infinite-dimensional anti-Kaehlerian space.

Contribution

It establishes the homogeneity of such submanifolds through a novel approach involving their complexification and infinite-dimensional analysis.

Findings

Homogeneity of the lift of the complexification is demonstrated.

The proof applies to submanifolds of codimension greater than one.

The method involves anti-Kaehlerian space techniques.

Abstract

In this paper, we show that an irreducible proper complex equifocal submanifold of codimension greater than one in a symmetric space of non-compact type. The proof is performed by showing the homogeneity of the lift of the complexification of the original submanifold to some infinite dimensional anti-Kahelerian space.