Adding a uniton via the DPW method

TL;DR

This paper explores how the addition of a uniton through the DPW method affects harmonic maps into symmetric spaces, focusing on finite type properties and their preservation.

Contribution

It introduces a novel perspective on adding unitons via the DPW method and proves finite type preservation for Gauss bundles of harmonic maps into Grassmannians.

Findings

Gauss bundle of finite type harmonic maps into Grassmannians remains finite type.

The DPW method provides a new framework for understanding uniton addition.

Finite type property is preserved under certain uniton operations.

Abstract

In this paper we describe how the operation of adding a uniton arises via the DPW method of obtaining harmonic maps into compact Riemannian symmetric spaces out of certain holomorphic one forms. We exploit this point of view to investigate which unitons preserve finite type property of harmonic maps. In particular, we prove that the Gauss bundle of a harmonic map of finite type into a Grassmannian is also of finite type.