  This article uses Cartan-K\"ahler theory to construct local conservation laws
from covariantly closed vector valued differential forms, objects that can be
given, for example, by harmonic maps between two Riemannian manifolds. We apply
the article's main result to construct conservation laws for covariant
divergence free energy-momentum tensors. We also generalize the local isometric
embedding of surfaces in the analytic case by applying the main result to
vector bundles of rank two over any surface.
