Abstract For a Spin (9)-structure on a Riemannian manifold M 16 we write explicitly the
matrix ψ of its Kähler 2-forms and the canonical 8-form Φ Spin (9). We then prove that Φ …

We deal with Riemannian properties of the octonionic Hopf fibration S 15→ S 8, in terms of
the structure given by its symmetry group Spin (9). In particular, we show that any vertical …

TheHermitian symmetric spaceM= EIII appears in the classification of complete simply
connected Riemannian manifolds carrying a parallel even Clifford structure [19]. This means …

This is a survey on the construction of a canonical or “octonionic Kähler” 8-form,
representing one of the generators of the cohomology of the four Cayley-Rosenfeld …

arXiv:1511.06239v3 [math.DG] 12 Sep 2016 Page 1 CLIFFORD SYSTEMS IN
OCTONIONIC GEOMETRY MAURIZIO PARTON, PAOLO PICCINNI, AND VICTOR …

Starting from the 2001 Thomas Friedrich's work on Spin (9), we review some interactions
between Spin (9) and geometries related to octonions. Several topics are discussed in this …

In this paper we show that for a generalized Berger metric $\hat {g} $ on $ S^ 3$ close to the
round metric, the conformally compact Einstein (CCE) manifold $(M, g) $ with $(S^ 3,[\hat …

Two explicit expressions of the canonical 8-form on a Riemannian manifold with holonomy
group Spin (9) Spin (9) have been given: one by the present authors and another by Parton …

A classical theoremof Kervaire states that products of spheres are parallelizable if and only if
at least one of the factors has odd dimension. Two explicit parallelizations on S m× S 2 h− 1 …

We present a binary code for spinors and Clifford multiplication using non-negative integers
and their binary expressions, which can be easily implemented in computer programs for …