Trajectories on geodesic spheres in a non-flat complex space form (Q1021309)

A magnetic field on a Riemannian manifold \(M\) is defined by a closed \(2\)-form. On a Kähler manifold there are defined uniform magnetic fields which are constant multiples of the Kähler form. The author studies some basic properties of trajectories for canonical magnetic fields induced by the structure tensor on real hypersurfaces of types \(A_0\) and \(A_1\) in a complex space form. He obtains the extrinsic shapes of trajectories for canonical magnetic fields on these hypersurfaces as curves in a non-flat complex space form and shows that they are Killing helices of proper order not greater that \(4\). Moreover, he obtains the cases where the trajectories are closed. The study gives also informations on the moduli space of helices on real space forms.