LAGRANGIANS FOR RICCI-FLAT GEOMETRIES

The new non-chiral Lagrangian density for the Einstein field equations, which leads to Nester's frames and Hamiltonian formulations in Ashtekar variables, is shown to arise naturally as a canonical 4-form on the second frame bundle, of pure grade 4 in m = 4 Clifford algebra. This insight allows such Lagrangians to be written as easily for higher dimensional theories.