  Differential geometric structures such as the principal bundle for the
canonical vector bundle on a complex Grassmann manifold, the canonical
connection form on this bundle, the canonical symplectic form on a complex
Grassmann manifold and the corresponding dynamical systems are investigated.
The Grassmann manifold is considered as an orbit of the co-adjoint action and
the symplectic form is described as the restriction of the canonical Poisson
structure on a Lie coalgebra. The holonomy of the connection on the principal
bundle over Grassmannian and its relation with Berry phase is considered and
investigated for the integral curves of Hamiltonian dynamical systems.
