On constant mean curvature surfaces with periodic metric

Abstract

We investigate CMC-surfaces with periodic metric in a dressing orbit of the cylinder. It is shown, that such surfaces are always of finite type. Using the periodicity conditions for the extended frame of a CMC-surface, we develop an alternative approach to the classification of CMC-tori given by Pinkall and Sterling.

arXiv comment42 pages, LaTeX+amscd package, no figures