  A self-consistent non-minimal non-Abelian Einstein-Yang-Mills model,
containing three phenomenological coupling constants, is formulated. The ansatz
of a vanishing Yang-Mills induction is considered as a particular case of the
self-duality requirement for the gauge field. Such an ansatz is shown to allow
obtaining an exact solution of the self-consistent set of equations when the
space-time has a constant curvature. An example describing a pure magnetic
gauge field in the de Sitter cosmological model is discussed in detail.
