2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95109Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient conditions for a left-invariant connection on a Lie group to be the Levi-Civita connection of some semi-Riemannian metric on the group. As a special case, we will consider constant connections in $\R^n$.Article for the Proceedings of the EGEO2005, Cordoba, Argentina. LaTeX2e, amsart, 9 pages, no figuresDifferential Geometrytext