Eine Kennzeichnung der Oktavenebene

Abstract

We consider partitions of R 16 into pairwise complementary 8-dimensional subspaces whose union covers R 16 (or, equivalently, fiberings of S15 by great 7-spheres). It is shown that if such a partition is (globally) invariant by a closed subgroup of GL16(R) locally isomorphic to S07(IR, I), then it is linearly equivalent to the classical Hopf partition corresponding to the Cayley numbers O, namely the system of lines through the origin in the affine Cayley plane over O.