[en] The Einstein equations are written in the form of equalities for O(1, 3) invariant components of the curvature tensor field. The 'material part' of the curvature is expressed in terms of the energy-momentum tensor field. In this approach the self-gravitating Yang-Mills fields are considered, and a reduced set of equations is obtained for them in the general form. In the spherically symmetric space-time the equations are written explicitly for the SU(2) gauge group. It is shown that the Bianchi identities allow one to except some of the gauge field equations