  Two classic field theories of metric gravitation are given as
constant-coefficient Exterior Differential Systems (EDS) on the flat
orthonormal frame bundle over ten dimensional space. They are derivable by
variation of Cartan 4-forms, and shown to be well-posed by calculation of their
Cartan characteristic integers. Their solutions are embedded Riemannian
4-spaces. The first theory is generated by torsion 2-forms and Ricci-flat
3-forms and is a constant-coefficient EDS for vacuum tetrad gravity; its Cartan
character table is the same as found for an EDS recently given in terms of
tetrad frame and connection variables [1] [2]. The second constant-coefficient
EDS is generated solely by 2-forms, and has a Cartan form of quadratic
Yang-Mills type. Its solutions lie in torsion free 6-spaces and are fibered
over 3-spaces. We conjecture that these solutions may be classically related to
10-dimensional quantum field theoretic constructions of cosmological vacua [3].
