A aplicação de Gauss de superfícies completas em R3 e R4

Abstract

We divide this work into two chapters. In Chapter 1, we give the preliminaries about surfaces in R3 and Riemann surfaces without much demonstration since the subject has already been exhaustively presented in several books. Also in chapter 1, we will demonstrate the theorem I. In chapter 2, we present some basic facts about the geometry of surfaces in R4 and because it is a subject not very seen we demonstrate almost everything that is affirmed. Finally, we conclude the chapter with the proof of Theorem II, the main objective of this monograph.