  We present two families of exterior differential systems (EDS) for causal
embeddings of orthonormal frame bundles over Riemannian spaces of dimension q =
2,3,4,5.. into orthonormal frame bundles over flat spaces of higher dimension.
We calculate Cartan characters showing that these EDS are dynamical field
theories. The first family includes a new non-isometric embedding EDS for
classical Einstein vacuum relativity (q = 4). The second, generated only by
2-forms, is a family of classical "stringy" or Kaluza-type (q = 5) integrable
systems. Cartan forms are found for all these dynamical systems.
