A theorem of Hadamard-Cartan type for Kahler magnetic fields

摘要

We study the global behavior of trajectories for Kahler magnetic fields on a connected complete Kaehler manifold M of negative curvature. Concerning these trajectories we show that theorems of Hadamard-Cartan type and of Hopf-Rinow type hold: If sectional curvatures of M are not greater than c (< 0) and the strength of a Kahler magnetic field is not greater than √∣c∣, then every magnetic exponential map is a covering map. Hence arbitrary distinct points on M can be joined by a minimizing trajectory for this magnetic field.