  It is considered, in the framework of constrained systems, the quantum
dynamics of non-relativistic particles moving on a d-dimensional Riemannian
manifold M isometrically embedded in $R^{d+n}$. This generalizes recent
investigations where M has been assumed to be a hypersurface of $R^{d+1}$. We
show, contrary to recent claims, that constrained systems theory does not
contribute to the elimination of the ambiguities present in the canonical and
path integral formulations of the problem. These discrepancies with recent
works are discussed.
