A factorization of harmonic maps into Semisimple Lie groups

TL;DR

This paper presents a method to decompose harmonic maps into semisimple Lie groups into simpler harmonic maps based on the Iwasawa decomposition, facilitating the study of such maps.

Contribution

It introduces a factorization technique for harmonic maps into semisimple Lie groups, enabling analysis via component maps from the Iwasawa decomposition.

Findings

Factorization of harmonic maps into components of the Iwasawa decomposition

Application to harmonic maps from Euclidean space into SL(2,R)

Enhanced understanding of harmonic maps into semisimple Lie groups

Abstract

We factorize harmonic maps with values in a semisimple Lie groups in a product of harmonic maps with values in the components of the Iwasawa decomposition. In particular, we use this factorization to study the harmonic maps from $\mathbb{R}^n$ into $SL(2,\mathbb{R})$.