In this thesis, we study a Bäcklund transformation for minimal surfaces - surfaces with vanishing mean curvature - transforming a given minimal surface into a possible infinity of new ones. The transformation, also carrying with it mappings between solutions to the elliptic Liouville equation, is first derived by using geometrical concepts, and then by using algebraic methods alone - the latter we have not been able to find elsewhere. We end by exploiting the transformation in an example, transforming the catenoid into a family of new minimal surfaces.

Made available in DSpace on 2014-07-29T16:02:16Z (GMT). No. of bitstreams: 1 Dissertacao Leonardo Antonio Souto.pdf: 432603 bytes, checksum: cab235c5136d13c6ddcc4340d691a745 (MD5) Previous issue date: 2008-02-29 / 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. / A teoria da transformação de Ribaucour para hipersuperfícies em formas espaciais é apresentada. É mostrado um método para obter superfícies linear Weingarten em formas espaciais tridimensionais. Aplicando a teoria da transformações de Ribaucour ao cilindro, obtemos uma família à dois parâmetros de superfícies linear Weingarten. Uma nova família à um parâmetro de superfícies com curvatura média constante completas na esfera unitária, localmente associada ao toro plano é obtida. Construimos uma família de superfícies com curvatura média constante igual a 1 no espaço hiperbólico tridimensional que são localmente associadas a prima da superfície de Enneper.