  We briefly review the concepts of generalized zero curvature conditions and
integrability in higher dimensions, where integrability in this context is
related to the existence of infinitely many conservation laws. Under certain
assumptions, it turns out that these conservation laws are, in fact, generated
by a class of geometric target space transformations, namely the
volume-preserving diffeomorphisms. We classify the possible conservation laws
of field theories for the case of a three-dimensional target space. Further, we
discuss some explicit examples.
