Frame bundles: Covariance, invariant forms and exterior differential systems for Ricci-flat solutions

The authors have recently advocated the study of invariant differential systems, which are related to Kac-Moody algebras and possible generalizations, to understand soluble nonlinear evolution equations. A result obtained by Sparling and Chinea in spinor language shows in fact that the equations of Ricci-flatness, when m=4, are elegantly expressed as an invariant differential system in ω/sup i/ and ω/sub jk//sup i/. This work has been extended by Gurses and Bilge to include the cosmological constant, and an Einstein-Maxwell field. The authors return to these systems at the end, and also mention how some prolongations found for them appear in the present general invariant formalism