Lax-type flows on Grassmann manifolds and dual momentum mappings

A general approach to building integrable Lax-type flows on Grassmann manifolds, based on the momentum mapping reduction theory, is developed. All of the flows are shown to be Hamiltonian with respect to different symplectic structures generated by dual special Hamiltonian actions on Grassmann manifolds. As a by-product of the approach a natural connection associated with dual momentum mappings is constructed explicitly via one Uhlmannʹs procedure.