Bundle of Hamiltonian Metrics on an almost Quaternion Real Manifold

Hamiltonian metrics are introduced on an almost quaternion real manifold. It is proved that every almost quaternion para-compact real manifold admits a Hamiltonian metric. It is established that there is a bijective correspondence between the set of all Hamiltonj.an metrics on an almost quaternion real manifold of dimension 4m with respect to the -canonical almost quaternion structure and the homogeneous space Θ{GL(m,H)}/Θ{Sp(m)}.