Not yet Determined Manuscript-nr. Remarks on the Darboux Transform of Isothermic Surfaces

We study Darboux and Christooel transforms of isothermic surfaces in Euclidean space. These transformations play a signiicant role in relation to integrable system theory. Surfaces of constant mean curvature turn out to be special among all isothermic surfaces: their parallel constant mean curvature surfaces are Christooel and Darboux transforms at the same time. We prove | as a generalization of Bianchi's theorem on minimal Darboux transforms of minimal surfaces | that constant mean curvature surfaces in Euclidean space allow 1 3 Darboux transforms into surfaces of constant mean curvature. We indicate the connection of these Darboux transforms to BB acklund transforms of spherical surfaces.