Corchete y Curvatura

The first part of this article presents the definition of Lie Bracket related to commuting flows of vector fields. In the second part, basic definitions and of connections and curvature are given in order to emphasize the link bet- ween Lie Brackets and curvature. Finally, by using locally-defined connections, we give a short and original proof of a classical theorem of Beltrami. The article is addressed to a non specialist in local differential geometry