Hokkaido Mathematical Journal

BAI Pengfei, ADACHI Toshiaki,

An estimate of the spread of trajectories for Kähler magnetic fields.

Hokkaido Mathematical Journal, 42 (2013) pp.445-462

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Abstract

On a Kähler manifold we consider trajectories under the influence of Kähler magnetic fields. They are smooth curves which are parameterized by their arclengths and whose velocities and normal vectors form complex lines. In this paper we study how trajectories spread, and give an estimate of norms of magnetic Jacobi fields from below and an estimate of area elements of trajectory-spheres.

MSC(Primary)53C22
MSC(Secondary)53C20
Uncontrolled KeywordsKähler magnetic fields, magnetic Jacobi fields, trajectory-spheres, area elements, comparison theorems