Abstract: Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kähler manifolds, and the Hamiltonian mechanics on Kähler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton's equations was obtained, and so on.

Key words: Kä, hler manifold, connection, absolute differential, Lie derivative, Hamiltonian
vector, 1-parameter group