In his paper [Nagoya Math. J. 60, 180-188 (1976; Zbl 0305.53046)], K. Nomizu characterized totally geodesic complex projective spaces among Kähler submanifolds of a complex projective space using an extrinsic property of geodesics. The introduction of the paper presents a review of results on the characterization of submanifolds by the extrinsic shape of some families of curves in the submanifold. The authors characterize totally geodesic Kähler submanifolds of an arbitrary Kähler manifold by the extrinsic shape (in the manifold) of trajectories of a Kähler magnetic field on the submanifold. Then using the same technique they characterize planar geodesic immersions of the Cayley projective plane \(CaP^2\) into a real space form.