Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 169

On the meromorphic potential for a harmonic surface in a k-symmetric space.

J. Dorfmeister, I. McIntosh, F. Pedit, H. Wu

Every harmonic map of a simply connected domain into a symmetric space can be described by rank (of the symmetric space) many meromorphic functions, its meromorphic potential. In this note we give a formula for the meromorphic potential in terms of solutions to the complexified harmonic map equations. In particular this identifies the meromorphic potentials for surfaces of constant mean curvature obtained by dressing the cylinder (e.g. all constant mean curvature tori).

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