El teorema de inmersión de Bonnet

Abstract

[en] This paper deals with a classic theorem in differential geometry of surfaces: Bonnet’s theorem. Our objective is to generalize the theorem for manifolds of arbitrary codimension. The theory of vector bundles gives us strong tools concerning different topics in differentialgeometry theory, such as metric, connections and curvature. Henceforth, we develop in the first part of this work the most important aspects in this theory, without loosing sight of our objectives. We will introduce one of the most powerful tools in this theory: the pullback of vector bundles. This tool will be frequently used during this work. Moreover, we will shortly introduce the concept of Ehresmann connection, whose presence in modern differential geometry is highly important. At the end, it will be given a precise statement and a proof of the Bonnet’s immersion theorem.