Generalized forms, metrics and Ricci flat four-metrics

Generalized differential forms are used in discussions of metric geometries and Einstein’s vacuum field equations. Cartan’s structure equations are generalized and applied. In particular flat generalized connections are associated with any metric. Einstein’s vacuum field equations and their Lorentzian four-metric solutions are considered from a novel point of view. It is shown how particular flat generalized connections and geometries can encode such Ricci flat metrics.