A theorem of Hadamard-Cartan type for Kähler magnetic fields (Q455014)

The author studies the global behavior of trajectories for Kähler magnetic fields on a connected complete Kähler manifold \(M\) of negative curvature. He shows that theorems of Hadamard-Cartan type and of Hopf-Rinow type hold for such trajectories. More precisely, if the sectional curvatures of \(M\) are not greater than \(c\) (\(< 0\)) and the strength of a Kähler magnetic field is not greater than \(\sqrt{|c|}\), 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.