All harmonic 2-spheres in the unitary group, completely explicitly
2009; Springer Science+Business Media; Volume: 266; Issue: 4 Linguagem: Inglês
10.1007/s00209-009-0607-7
ISSN1432-1823
AutoresMaria João Ferreira, Bruno Ascenso Simões, John Carter Wood,
Tópico(s)Geometry and complex manifolds
ResumoWe 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 $${\bar{\partial}}$$ -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.
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