Darboux transforms and simple factor dressing of constant mean curvature surfaces

Francis E Burstall, J F Dorfmeister, K Leschke, Aurea C Quintino

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)213-236
Number of pages14
JournalManuscripta Mathematica
Volume140
Issue number1-2
Early online date22 Feb 2012
DOIs
Publication statusPublished - Jan 2013

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