2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67776In this paper, we study the moduli spaces $\mathcal{M}_{δ,c_2}$ of stable rank-2 vector bundles on non-K\" ahler elliptic surfaces, thus giving a classification these bundles; in the case of Hopf and Kodaira surfaces, these moduli spaces admit the structure of an algebraically completely integrable Hamiltonian system.15 pages, shortened version, small corrections were madeAlgebraic GeometryComplex Variables14J60; 14D21, 14D22, 14F05,14J27, 32G13, 32J15, 14H70text