Extended solutions of the harmonic map equation in the special unitary group

TL;DR

This paper classifies all finite uniton harmonic maps from Riemann surfaces into SU(n) using Bruhat decomposition and describes their Frenet frame data, advancing understanding of harmonic map structures.

Contribution

It provides a complete classification of harmonic maps into SU(n) based on algebraic loop decompositions and details their Frenet frame data.

Findings

Classification of harmonic maps via Bruhat decomposition

Explicit description of Frenet frame data for these maps

Framework for analyzing harmonic maps in SU(n)

Abstract

We classify all harmonic maps of finite uniton number from a Riemann surface into SU(n) in terms of certain pieces of the Bruhat decomposition of the subgroup of algebraic loops in SU(n). We give a description of the "Frenet frame data" for such harmonic maps in a given class.