TY - JOUR

T1 - Darboux transforms and simple factor dressing of constant mean curvature surfaces

AU - Burstall, Francis E

AU - Dorfmeister, J F

AU - Leschke, K

AU - Quintino, Aurea C

PY - 2013/1

Y1 - 2013/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84871999925&partnerID=8YFLogxK

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

U2 - 10.1007/s00229-012-0537-2

DO - 10.1007/s00229-012-0537-2

M3 - Article

VL - 140

SP - 213

EP - 236

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1-2

ER -