Vacuum Einstein Equations in Terms of Curvature Forms
  A closed explicit representation of the vacuum Einstein equations in terms of components of curvature 2-forms is given. The discussion is restricted to the case of non-vanishing cubic invariant of conformal curvature spinor. The complete set of algebraic and differential identities connecting particular equations is presented and their consistency conditions are analyzed. 
Yuri N. Obukhov and Sergey I. Tertychniy