# Darboux transforms and simple factor dressing of constant mean curvature surfaces - Mathematics > Differential Geometry

Darboux transforms and simple factor dressing of constant mean curvature surfaces - Mathematics > Differential Geometry - Download this document for free, or read online. Document in PDF available to download.

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.

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

Source: https://arxiv.org/