Isothermic Surfaces Associated with the Cylinder Obtained by Ribaucour Transformations

In this paper we consider a method for obtaining isothermic surfaces based on the Ribaucour transformations. By applying the theory to the cylinder, we obtain two families of complete isothermic surfaces. In the first family we have bubbletons surfaces and surfaces with planar ends. In second family, we get Dupin surfaces. As an application, we provide new explicit solutions to the Calapso equation.