Uma caracterização da A-equivalência entre aplicações de Gauss de variedades orientáveis em termos de equivalência Lagrangiana e funções altura

Abstract

We will present in this dissertation a Gauss map study to provide a characterization of the A-equivalence between Gauss maps of oriented manifolds in terms of height function. For this we are going to develop concepts that will be necessary to see Gauss map as a Lagrangian map, here we will need to define Lagrangian submanifolds, equivalent Lagrangian maps, generating families and the equivalences between them. We also have to show that the Gauss map is a catastrophe map associated with height functions, here we will need to define what a catastrophe manifold and catastrophe map to later conclude that two Gauss map are A-equivalent if and only if the germs of their generating families are R+-equivalent