Harmonic maps into the orthogonal group and null curves

TL;DR

This paper develops algebraic parametrizations for harmonic maps into the orthogonal group O(n) with finite uniton number, linking them to null curves and minimal surfaces via free holomorphic data.

Contribution

It introduces explicit algebraic formulas for harmonic maps into O(n) and uncovers a novel connection with null curves and minimal surfaces.

Findings

Provided algebraic parametrizations for harmonic maps into O(n)

Established a correspondence between harmonic maps and null curves

Linked harmonic maps to minimal surface representations

Abstract

We find algebraic parametrizations of extended solutions of harmonic maps of finite uniton number from a surface to the orthogonal group O(n) in terms of free holomorphic data which lead to formulae for all such harmonic maps. Our work reveals an interesting correspondence between certain harmonic maps and the free Weierstrass representation of null curves and minimal surfaces in 3- and 4-space.