Local isometric imbeddings of $P^{2}(H)$ and $P^{2}(Cay)$

Abstract

We investigate local isometric imbeddings of the quaternion projective plane P 2 (H) and the Cayley projective plane P 2 (Cay) into the Euclidean spaces. We prove a non-existence theorem of local isometric imbeddings (see Theorem 2), by which we can conclude that the isometric imbeddings given in Kobayashi [8] are the least dimensional isometric imbeddings of P 2 (H) and P 2 (Cay).