The homogeneous slice theorem for the complete complexification of a proper complex equifocal submanifold

TL;DR

This paper studies the homogeneity properties of specific slices within the complete complexification of proper complex equifocal submanifolds in non-compact symmetric spaces.

Contribution

It introduces the homogeneous slice theorem for these complexified submanifolds, advancing understanding of their geometric structure.

Findings

Identifies conditions under which slices are homogeneous

Provides a new theorem characterizing slice homogeneity

Enhances comprehension of complex equifocal submanifold geometry

Abstract

We investigate the homogeneity of certain kind of slices of the complete complexification of a proper complex equifocal submanifold in a symmetric space of non-compact type.