Examples of a complex hyperpolar actions without singular orbit

TL;DR

This paper constructs and analyzes examples of complex hyperpolar actions on non-compact symmetric spaces that lack singular orbits, expanding understanding of their geometric properties.

Contribution

It provides the first known examples of complex hyperpolar actions without singular orbits and explores their geometric characteristics.

Findings

Constructed explicit examples of complex hyperpolar actions without singular orbits.

Analyzed the geometric structure of the orbits in these examples.

Enhanced understanding of the orbit geometry in non-compact symmetric spaces.

Abstract

The notion of a complex hyperpolar action on a symmetric space of non-compact type has recently been introduced as counterpart of a hyperpolar action on a symmetric space of compact type. In this paper, we construct examples of a complex hyperpolar action without singular orbit and investigate the geometry of the orbits of the examples.