English

Harmonic maps into the orthogonal group and null curves

Differential Geometry 2018-11-06 v3

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.

Keywords

Cite

@article{arxiv.1712.04665,
  title  = {Harmonic maps into the orthogonal group and null curves},
  author = {Maria João Ferreira and Bruno Ascenso Simões and John C. Wood},
  journal= {arXiv preprint arXiv:1712.04665},
  year   = {2018}
}

Comments

Some explanations improved and corrections made. Accepted for publication by Math. Z

R2 v1 2026-06-22T23:16:38.720Z