Hamilton dynamics and $H$-planar curves

An important example of Hamilton flows on K¨ahler manifold are H planar flows: all their trajectories are H -planar curves (complex analog of geodesics). The equation which has to obey the Hamiltonian of H planar flow is received and the method of finding general solution of this equation is proposed. Trajectories of charged particles in magnetic fields of special form on K¨ahler manifolds of constant holomorphic sectional curvature are studied. Using the fact that K¨ahler manifolds of constant holomorphic sectional curvature admit H -projective mapping on flat space C n the equation of particle motion is reduced to an ordinary differential equation of second order.