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July, 2012 A theorem of Hadamard-Cartan type for Kähler magnetic fields
Toshiaki ADACHI
J. Math. Soc. Japan 64(3): 969-984 (July, 2012). DOI: 10.2969/jmsj/06430969


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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Toshiaki ADACHI. "A theorem of Hadamard-Cartan type for Kähler magnetic fields." J. Math. Soc. Japan 64 (3) 969 - 984, July, 2012.


Published: July, 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1252.53047
MathSciNet: MR2965435
Digital Object Identifier: 10.2969/jmsj/06430969

Primary: 53C22
Secondary: 53B35

Keywords: Comparison theorem , Kähler magnetic fields , theorem of Hadamard-Cartan , theorem of Hopf-Rinow , Trajectories , trajectory-harps , trajectory-spheres

Rights: Copyright © 2012 Mathematical Society of Japan


Vol.64 • No. 3 • July, 2012
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