  Symmetric 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 $\R^n$.
