Trajectories on Geodesic Spheres in a Non-Flat Complex Space Form

In this paper we study some basic properties of trajectories for canonical magnetic fields induced by structure tensor on real hypersurfaces of types A0 and A1 in a complex space form. On each such real hypersurface, there are infinitely many canonical magnetic fields whose trajectories with null structure torsion are closed, and also infinitely many canonical magnetic fields whose trajectories with null structure torsion are open. We give a condition dividing canonical magnetic fields into these two classes and investigate lengths of closed trajectories. Our study also provide us information on the moduli space of Killing helices of proper order 4 on complex space forms.