On General Relativity extension
  The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills' equations for the curvature tensor. Einstein's equations (with cosmological term to appear as an integration constant) are contained in the theory proposed. New is that now gravitational field is not exceptionally determined by matter energy-momentum but can possess its own non-Einsteinian dynamics(vacuum fluctuations, self-interaction)which is generally an attribute of nonabelian gauge field. The gravitational equations proper due to either matter energy-momentum or vacuum fluctuations are side conditions imposed on the Riemann tensor, like self-duality conditions. 
A. L. Koshkarov