Resumen.
La primera parte del art\'{\i}culo presenta al corchete de Lie
asociado al problema de la comutatividad de dos flujos. En la segunda
parte se introducen las definiciones b\'asicas de conexi\'on y
curvatura en fibrados vectoriales, subrayando la relaci\'on
corchete-curvatura. Finalmente, usando conexiones afines localmente
definidas, se da una demostraci\'on original y sencilla de un teorema
de Eugenio Beltrami. Este art\'{\i}culo apunta a un lector no
especialista (e.g. un estudiante de doctorado en matem\'atica o
f\'{\i}sica, etc) en geometr\'{\i}a diferencial local.
Abstract.
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 between 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.
