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Abstract: We define a transformation on harmonic maps from a Riemann surface into the2-sphere which depends on a complex parameter, the so-called mu-Darbouxtransformation. In the case when the harmonic map N is the Gauss map of aconstant mean curvature surface f and the parameter is real, the mu-Darbouxtransformation of -N is the Gauss map of a classical Darboux transform f. Moregenerally, for all complex parameter the transformation on the harmonic Gaussmap of f is induced by a generalized Darboux transformation on f. We showthat this operation on harmonic maps coincides with simple factor dressing, andthus generalize results on classical Darboux transforms of constant meancurvature surfaces: every mu-Darboux transform is a simple factor dressing, andvice versa.



Autor: F. E. Burstall, J. F. Dorfmeister, K. Leschke, A. Quintino

Fuente: https://arxiv.org/







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