Hokkaido Mathematical Journal

Comparison theorems on trajectory-harps for Kähler magnetic fields which are holomorphic at their arches

Qingsong SHI and Toshiaki ADACHI

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Abstract

A trajectory-harp is a variation of geodesics associated with a trajectory. We estimate how trajectories for Kähler magnetic fields go away from their initial points and show how they are bended by comparing trajectory-harps on a Kähler manifolds with those on complex space forms. Under a condition on sectional curvatures, we show that when the length of a geodesic segment of a trajectory-harp coincides with that on a complex space form it forms a part of a totally geodesic complex line.

Article information

Source
Hokkaido Math. J., Volume 48, Number 2 (2019), 427-441.

Dates
First available in Project Euclid: 11 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1562810518

Digital Object Identifier
doi:10.14492/hokmj/1562810518

Mathematical Reviews number (MathSciNet)
MR3980951

Zentralblatt MATH identifier
07080103

Subjects
Primary: 53C22: Geodesics [See also 58E10]
Secondary: 53B35: Hermitian and Kählerian structures [See also 32Cxx]

Keywords
Kähler magnetic fields trajectory-harps string-length string-cosine zenith angles

Citation

SHI, Qingsong; ADACHI, Toshiaki. Comparison theorems on trajectory-harps for Kähler magnetic fields which are holomorphic at their arches. Hokkaido Math. J. 48 (2019), no. 2, 427--441. doi:10.14492/hokmj/1562810518. https://projecteuclid.org/euclid.hokmj/1562810518


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