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We investigate parallel isotropic immersions of an open submanifold of either the Cayley projective plane CayPðaÞ or its noncompact dual into a real space form ~ Mð~ cÞ, and give a characterization of the first standard embedding of CayPðaÞ into ~ Mð~ cÞ in terms of a particular class of Frenet curves of order 2.

Isotropic immersions of the Cayley projective plane and Cayley Frenet curves