2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152164We 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.42 pages, LaTeX+amscd package, no figuresDifferential Geometry53A10 (Primary) 58D19 (Secondary)text