On curvature-adapted and proper complex equifocal submaniflds

TL;DR

This paper studies a special class of submanifolds in non-compact symmetric spaces, focusing on their curvature properties and potential to characterize principal orbits of Hermann type actions.

Contribution

It introduces and analyzes curvature-adapted and proper complex equifocal submanifolds, linking them to principal orbits of Hermann type actions in symmetric spaces.

Findings

Contains principal orbits of Hermann type actions as examples

Provides groundwork for geometrical characterization of these orbits

Advances understanding of submanifold structures in symmetric spaces

Abstract

In this paper, we investigate a curvature-adapted and proper complex equifocal submanifold in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples. In future, the results in this paper will be used to give a submanifold geometrical characterization of principal orbits of Hermann type actions.