We study curves of order 2 from the viewpoint of submanifold theory. We give a characterization of the parallel Kähler embeddings of a complex projective space into an ambient complex projective space from this point of view. This characterization is an improvement of the results in [N, PS].
"A characterization of the second Veronese embedding into a complex projective space." Proc. Japan Acad. Ser. A Math. Sci. 77 (7) 99 - 102, Sept. 2001. https://doi.org/10.3792/pjaa.77.99