# Darboux transforms and simple factor dressing of constant mean curvature surfaces

### Reference:

Burstall, F. E., Dorfmeister, J. F., Leschke, K. and Quintino, A. C., 2013. Darboux transforms and simple factor dressing of constant mean curvature surfaces. *Manuscripta Mathematica*, 140 (1-2), pp. 213-236.

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### Official URL:

http://dx.doi.org/10.1007/s00229-012-0537-2

### Abstract

We define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surface f and the parameter is real, the mu-Darboux transformation of -N is the Gauss map of a classical Darboux transform f. More generally, for all complex parameter the transformation on the harmonic Gauss map of f is induced by a (generalized) Darboux transformation on f. We show that this operation on harmonic maps coincides with simple factor dressing, and thus generalize results on classical Darboux transforms of constant mean curvature surfaces: every mu-Darboux transform is a simple factor dressing, and vice versa.

### Details

Item Type | Articles |

Creators | Burstall, F. E., Dorfmeister, J. F., Leschke, K. and Quintino, A. C. |

DOI | 10.1007/s00229-012-0537-2 |

Departments | Faculty of Science > Mathematical Sciences |

Refereed | Yes |

Status | Published |

ID Code | 27062 |

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