English

Explicit construction of harmonic two-spheres into the complex Grassmannian

Differential Geometry 2010-07-26 v1

Abstract

We present an explicit description of all harmonic maps of finite uniton number from a Riemann surface into a complex Grassmannian. Namely, starting from a constant map QQ and a collection of meromorphic functions and their derivatives, we show how to algebraically construct all harmonic maps from the two-sphere into a given Grassmannian Gp(Cn)G_p(\mathbb C^n). In this setting the uniton number depends on QQ and pp and we obtain a sharp estimate for it.

Keywords

Cite

@article{arxiv.1007.4143,
  title  = {Explicit construction of harmonic two-spheres into the complex Grassmannian},
  author = {Maria Joao Ferreira and Bruno Ascenso Simoes},
  journal= {arXiv preprint arXiv:1007.4143},
  year   = {2010}
}
R2 v1 2026-06-21T15:52:17.251Z