Linhas de curvatura em superfícies algébricas do espaço euclidiano de dimensão três

Abstract

The present work aims to study the curvature lines on algebraic surfaces of dimension three euclidean space, based on the article "Lines of curvature on algebraic surfaces"of the authors Sotomayor and Garcia. We try to define, exemplify and illustrate a technique called algebraic surface compactification, used throughout the work to study the lines of curvature at infinity. We conclude with the global theorem of structural stability of algebraic surface, which generalizes the conditions of Gutierrez and Sotomayor theorem for compact surfaces.