Mathematische Zeitschrift

, Volume 272, Issue 1–2, pp 151–174 | Cite as

Explicit construction of harmonic two-spheres into the complex Grassmannian

Article

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 Q 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 \({G_p(\mathbb C^n)}\) . In this setting the uniton number depends on Q and p and we obtain a sharp estimate for it.

Keywords

Harmonic map Uniton Grassmannian Loop group 

Mathematics Subject Classification (2000)

Primary 58E20 Secondary 53C43 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Maria João Ferreira
    • 1
    • 2
  • Bruno Ascenso Simões
    • 1
    • 3
  1. 1.Centro de Matemática e Aplicações FundamentaisUniversidade de LisboaLisbonPortugal
  2. 2.Departamento de Matemática da FCULUniversidade de LisboaLisbonPortugal
  3. 3.Universidade Lusófona, Núcleo de Investigação em MatemáticaLisbonPortugal

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