Weierstrass-type representation for harmonic maps into general symmetric spaces via loop groups

Abstract

In [19] a method was presented, which constructs via loop group splittings all harmonic maps into a compact symmetric space. The present paper generalizes this method to all spaces $G/K$, where $G$ is an arbitrary Lie group (semisimple or not) and $K$ is the fixpoint group of some involution of $G$. The method is illustrated by a number of examples.