All harmonic 2-spheres in the unitary group, completely explicitly

作者：Ferreira Maria Joao; Simoes Bruno Ascenso; Wood John C^*

来源：Mathematische Zeitschrift, 2010, 266(4): 953-978.

DOI：10.1007/s00209-009-0607-7

• Harmonic map
• Uniton
• Grassmannian model

We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group U(n) in any dimension, and so all harmonic maps from the 2-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual partial derivative-problems or loop group factorizations. We interpret our constructions using Segal's Grassmannian model, giving an explicit factorization of the algebraic loop group, and showing how to obtain harmonic maps into a Grassmannian.

• 出版日期2010-12