Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
DI SCALA, Antonio J.. Corchete y curvatura. Rev.colomb.mat. [online]. 2005, vol.39, n.2, pp. 113-131. ISSN 0034-7426.
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.
Palavras-chave : Lie Bracket; curvature tensor; a±ne connection.