Horocyclic Circles and Tubes around Complex Hypersurfaces in a Complex Hyperbolic Space

We show that every horocyclic circle of nonzero complex torsion on a complex hyperbolic space is expressed by a trajectory for a Sasakian magnetic field on some tube around totally geodesic complex hypersurface and that such an expression is unique up to the action of isometries on the complex hyperbolic space.