2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194302A 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.6 pages, no figures, accepted for publication in Gravitation and CosmologyGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext