Completely Explicit Formulae for Harmonic 2-spheres in the Unitary Group and Related Spaces
نویسندگان
چکیده
We describe the explicit construction of M. J. Ferreira, B. A. Simões and the author of all harmonic maps from the 2-sphere to the unitary group in terms of freely chosen meromorphic functions. The harmonic maps are displayed as the product of unitons with an explicit spanning set for each uniton given by an algebraic formula in terms of the meromorphic data. We then discuss an extension of this construction by M. Svensson and the author to general factorizations for the unitary group, showing how to find explicit formulae for harmonic maps into the orthogonal and symplectic groups.
منابع مشابه
S ep 2 00 9 ALL HARMONIC 2 - SPHERES IN THE UNITARY GROUP , COMPLETELY EXPLICITLY
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 ∂-problems or loop group factorizations. We interpret ...
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