Abstract
We study the global behavior of trajectories for Kähler magnetic fields on a connected complete Kähler 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 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.
Citation
Toshiaki ADACHI. "A theorem of Hadamard-Cartan type for Kähler magnetic fields." J. Math. Soc. Japan 64 (3) 969 - 984, July, 2012. https://doi.org/10.2969/jmsj/06430969
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