Kodai Mathematical Journal

Behaviors of circular trajectories on hypersurfaces of type (A1) in a complex hyperbolic space

Tuya Bao and Toshiaki Adachi

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We study circular trajectories for Sasakian magnetic fields on geodesic spheres, horospheres and tubes around totally geodesic complex hypersurfaces in a complex hyperbolic space. Investigating their extrinsic shapes in the ambient complex hyperbolic space, we give conditions for them to be bounded and to be closed. By use of information on lengths of circles in complex space forms, we give expressions of lengths of circular trajectories on those real hypersurfaces and show that their length spectrum is a discrete subset of a real line.

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Kodai Math. J., Volume 34, Number 3 (2011), 485-504.

First available in Project Euclid: 10 November 2011

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Bao, Tuya; Adachi, Toshiaki. Behaviors of circular trajectories on hypersurfaces of type ( A 1 ) in a complex hyperbolic space. Kodai Math. J. 34 (2011), no. 3, 485--504. doi:10.2996/kmj/1320935555. https://projecteuclid.org/euclid.kmj/1320935555

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