On Ribaucour transformations and minimal surfaces

Obtaining minimal surfaces by a Ribaucour transformation requires solving a sys-tem of partial dierential equations, which is a Darboux transformation. We consider the system in complex variables for minimal surfaces parametrized by isothermal co-ordinates and lines of curvature. We relate the data of the Enneper-Weierstrass representation of minimal surfaces associated by Ribaucour transformations. The system of equations is solved explicitly for a special class of surfaces, which include important minimal surfaces. The class is characterized in terms of the Weierstrass data. The application of these results to the helicoid provides a new family of com-plete, minimal surfaces, of genus zero, immersed in R3, with an innite number of embedded planar ends