About the theory on transformations of surfaces with constant curvature / Sobre a teoria das transformações de superfícies de curvatura constante

AUTOR(ES)

Gabriela Pereira Sander

DATA DE PUBLICAÇÃO

2009

RESUMO

The theory on transformations of surfaces with constant curvature begins, in the late nineteen century, with the article [3] of A.V. Bäcklund and, after, received important contributions from various geometricians, among others, L. Bianchi and C. Guichard (see, for example, [5, 6, 7, 17]). In this dissertation we outline some of the most important results on the theory of surfaces of constant mean (or gaussian) curvature. Such surfaces are associated to the solutions of nonlinear partial differential equations of second order. The analytic interpretation of the theory on transformations of constant curvature surfaces provides a method of obtaining, from a given solution of these partial differential equations, a new solution of the same equation, by integrating a system of differential equations, called Bäcklund transformation. Then, the permutability theorems give a "superposition formula" to construct, algebraically, new solutions

ASSUNTO(S)

transformation of surfaces trnasformação de superfícies constant curvature curvatura constante congruência congruence

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