Parallelizations on products of spheres and octonionic geometry : Complex Manifolds

摘要

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 Sm × S2h?1 seem to be quite natural, and have been previously studied by the first named author in [32]. The present paper is devoted to the three choices G = G2, Spin(7), Spin(9) of G-structures on Sm × S2h?1, respectively with m + 2h ? 1 = 7, 8, 16 and related with octonionic geometry.