Transformações de Ribaucour para hipersuperfícies em formas espaciais

Abstract

The theory of Ribaucour transformations for hypersurfaces in space forms is presented. A method to obtaining linear Weingarten surfaces in a three-dimensional space form is showed. By applying the theory to the cylinder, we obtain a two-parameter family of linear Weingarten surfaces. A new one-parameter family of complete constant mean curvature surfaces in the unit sphere, locally associated to the flat torus, is obtained. We construct new families of constant mean curvature 1 (cmc-1) surfaces which are locally associated to Enneper cousin.