Hokkaido Mathematical Journal

An estimate of the spread of trajectories for Kähler magnetic fields

Pengfei BAI and Toshiaki ADACHI

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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.

Article information

Source
Hokkaido Math. J., Volume 42, Number 3 (2013), 445-462.

Dates
First available in Project Euclid: 12 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1384273392

Digital Object Identifier
doi:10.14492/hokmj/1384273392

Mathematical Reviews number (MathSciNet)
MR3137395

Zentralblatt MATH identifier
1281.53041

Subjects
Primary: 53C22: Geodesics [See also 58E10]
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Keywords
Kähler magnetic fields magnetic Jacobi fields trajectory-spheres area elements comparison theorems

Citation

BAI, Pengfei; ADACHI, Toshiaki. An estimate of the spread of trajectories for Kähler magnetic fields. Hokkaido Math. J. 42 (2013), no. 3, 445--462. doi:10.14492/hokmj/1384273392. https://projecteuclid.org/euclid.hokmj/1384273392


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