Stable bundles on non-Kahler elliptic surfaces

In this paper, we study the moduli spaces ${\mathcal{M}}_{\delta ,c_2}$ 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.