Extrinsic circular trajectories on geodesic spheres in a complex projective space

We say a trajectory for a Sasakian magnetic field on a geodesic sphere in a complex projective space to be extrinsic circular if it can be seen as a circle in the ambient space. We study how the moduli space of extrinsic circular trajectories behaves in the moduli space of all circles in the ambient complex projective space. As an application we characterize the geodesic sphere of special radius which lies on the boundary position of the family of Berger spheres among all geodesic spheres and that has a characteristic properties from the viewpoint of lengths of circles.