Trajectories of charged particles in Kähler magnetic fields
The author investigates Hamiltonian flows on a Kähler manifold whose flow lines are \(H\)-planar curves. This means that the covariant derivative of the tangent \(\gamma'\) of every such flow line is contained in the complex line spanned by \(\gamma'\). He derives some equivalent local formulations of this condition and shows that the gradient flow lines of such a Hamiltonian function \(\kappa\) are \(H\)-planar as well. Finally he computes some more explicit formula for the flow lines of a Kähler magnetic field on a pseudo-Kähler manifold of constant holomorphic curvature. No applications of this local representation are given.
scientific article; zbMATH DE number 1091052