2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51676We 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.12 pages; More explicit title; two figures available from authorHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext