Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 286

Investigation and application of the dressing action on surfaces of constant mean curvature

J. Dorfmeister, G. Haak

We investigate the dressing action on surfaces of constant mean curvature (CMC surfaces) in Euclidean space. In particluar, we show that for CMC surfaces with umbilics the isotropy group under dressing is always trivial. This result is applied to the investigation of CMC surfaces whose metric is invariant under a group of automorphisms of the parameter domain.

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