Complete minimal submanifolds of compact Lie groups

TL;DR

This paper introduces a novel method utilizing harmonic morphisms and Lie group representation theory to construct complete minimal submanifolds within compact Lie groups and their quotients, exemplified by the special unitary groups.

Contribution

The paper presents a new technique for creating complete minimal submanifolds in compact Lie groups using harmonic morphisms and representation theory, expanding the toolkit for geometric analysis.

Findings

Constructed numerous examples of minimal submanifolds in special unitary groups.

Demonstrated the effectiveness of harmonic morphisms in submanifold construction.

Provided a general framework applicable to various compact Lie groups.

Abstract

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our method to construct many examples of compact minimal submanifolds of the special unitary groups.