Fibrados Vectoriales: el fundamento detrás de la geometría diferencial

Abstract

The following work has the purpose of making an intuitive and easy to understand theoretical introduction about vector bundles, using as a resource differential geometry and the relationship between these two areas of mathematics. Establishing in principle the basic concepts of a bundle, the object that precedes the vector bundle and from where the latter arises. In addition, the theory of tangent fibers and vector fields on smooth varieties is constructed, connecting the terms by means of a proposition, which constructs a tangent fiber as a vector fiber and establishing examples to visualize this result. The approach that the paper seeks to develop is by means of graphs, figures, illustrations and correspondences, so that it is interactive and visually appealing to the reader. Bundle theory is a recent area in mathematics and generates several important results for physics, topology and algebraic geometry.