Geometry of submanifolds in terms of behavior of geodesics (Q1346793)

Riemannian submanifolds \(M\) of a Riemannian manifold \(\widetilde {M}\) can be studied in terms of the behavior of geodesics in \(M\). The present paper characterizes parallel immersions of a Cayley projective plane into a sphere among isotropic immersions. Further it is shown that complex hypersurfaces with parallel second fundamental form are characterized by a geometric condition weaker than ``circular geodesic'' (= every geodesic of \(M\) is a circle in \(\widetilde {M}\)).