Special Isothermic Surfaces

In this work one can find a research on special isothermic surfaces of arbitrary type, and arbitrary codimension. The invariant formulation of special isothermic surfaces in the conformal n-sphere presented here gives a generalization of the notion, introduced by Darboux and Bianchi, in the beginning of 20th century, of special isothermic surfaces in a 3-dimensional space-form. We present a study of Darboux transforms, Christoffel transforms and T-transforms of a special isothermic surface in order to find out the behavior of these transformations. We establish necessary and sufficient conditions for surfaces of revolution, cones and cylinders to be special isothermic surfaces. The existence of formal Laurent series with the analogous property of polynomial conserved quantities (the characterization of special isothermic surfaces) is now guaranteed. Finally, we present a brief study about the discretization of the theory of special isothermic surfaces.EThOS - Electronic Theses Online ServiceGBUnited Kingdo