Superfícies mínimas de Laguerre e geometria isotrópica
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Data
2016-02-29
Autores
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Universidade Federal de Goiás
Resumo
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.
Descrição
Palavras-chave
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
Citação
Edwin Salinas Reyes. Superfícies mínimas de Laguerre e geometria isotrópica. 2016. 65 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.