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

Abstract

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.

Structure torsions of trajectories on real hypersurfaces of exceptional type in complex projective space

“…They characterize these real hypersurfaces by properties of circular trajectories. In their papers [3] and [4] they estimated the length of circular trajectories on real hypersurface of type (A 1 ) in a complex projective space and in a complex hyperbolic space. They studied the trajectories under Sasakian magnetic field on real hypersurfaces of type (B) in a complex hyperbolic space in [5] and [6].…”