Trajectories on real hypersurfaces of type (A2) which can be seen as circles in a complex hyperbolic space

Abstract

We study trajectories for Sasakian magnetic fields on homogeneous tubes around totally geodesic complex submanifolds in a complex hyperbolic space. We give conditions that they can be seen as circles in a complex hyperbolic space, and show how the set of their congruence classes are contained in the set of those of circles. In view of geodesic curvatures and complex torsions of circles obtained as extrinsic shapes of trajectories, we characterize these tubes among real hypersurfaces in a complex hyperbolic space.