Starting from the 2001 Thomas Friedrich’s work on
, we review some interactions between
and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the
canonical 8-form and its analogies with quaternionic geometry as well as the role of
both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel
manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley–Rosenfeld planes and to three series of Grassmannians.
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