Superfícies mínimas de Laguerre e geometria isotrópica

• Autor(a) principal: Reyes, Edwin Oswaldo Salinas
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/5832
• topic: Geometria isotrópica; Geometria de Laguerre; Superfícies mínimas de Laguerre e isotrópica; Funções bi-harmônicas; Transformações e superfícies de Legendre; Métrica dual; Isotropic geometry; Laguerre geometry; Minimal surfaces Laguerre and isotropic; Bi-harmonic functions; Transformations and surfaces Legendre, dual metric; Uual metric; ALGEBRA::GEOMETRIA ALGEBRICA

In this work we refer to the study of a new method and simple approach to minimal surface Laguerre in isotropic model of Laguerre geometry as the bi-harmonic function graph. We developed the isotropic geometry which studies the geometric properties invariant under certain affine transformations in Euclidean space, and the fundamental elements of Laguerre geometry which are spheres orienteds and plans orienteds, and properties which are invariant on the transformation of Laguerre. In addition, we will show a close relationship between minimal surfaces Laguerre spherical type and isotropic minimal surfaces which are given by the graph of harmonic functions and minimal Euclidean surfaces. Finally, the duality metric in the isotropic space is used to develop an isotropic exchange for minimal surfaces Laguerre in certain Lie transformation of Laguerre minimal surfaces in Euclidean space.