  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.
