Communications in Analysis and Geometry

Volume 22 (2014)

Number 3

Dressing transformations of constrained Willmore surfaces

Pages: 469 – 518



Francis E. Burstall (Department of Mathematical Sciences, University of Bath, United Kingdom)

Áurea C. Quintino (Centro de Matemática e Aplicações Fundamentais da Universidade, Lisboa, Portugal)


We use the dressing method to construct transformations of constrained Willmore surfaces in arbitrary codimension. An adaptation of the Terng-Uhlenbeck theory of dressing by simple factors to this context leads us to define Bäcklund transforms of these surfaces for which we prove Bianchi permutability. Specializing to codimension 2, we generalize the Darboux transforms of Willmore surfaces via Riccati equations, due to Burstall-Ferus-Leschke-Pedit-Pinkall, to the constrained Willmore case and show that they amount to our Bäcklund transforms with real spectral parameter.

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