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.