### A theorem of Hadamard-Cartan type for Kähler magnetic fields

Source: J. Math. Soc. Japan Volume 64, Number 3 (2012), 969-984.

#### 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.

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Primary Subjects: 53C22
Secondary Subjects: 53B35
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1343133751
Digital Object Identifier: doi:10.2969/jmsj/06430969
Mathematical Reviews number (MathSciNet): MR2965435

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