Isotropic immersions of the Cayley projective plane and Cayley Frenet curves

Abstract

We investigate parallel isotropic immersions of an open submanifold of either the Cayley projective plane CayP2(α) or its noncompact dual into a real space form $\tilde{M}^n(\tilde{c})$, and give a characterization of the first standard embedding of CayP2(α) into $\tilde{M}^n(\tilde{c})$ in terms of a particular class of Frenet curves of order 2.