Lengths of circular trajectories on geodesic spheres in a complex projective space

Abstract

We study trajectories for Sasakian magnetic fields which are also circles of positive geodesic curvature on geodesic spheres in a complex projective space. Investigating their extrinsic shapes we give a condition for them to be closed. By use of information on lengths of circles on a complex projective space, we give their lengths, and estimate the bottom of the length spectrum of circular trajectories.