Parallelizations on products of spheres and octonionic geometry
01 Pubblicazione su rivista
ISSN: 2300-7443
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^{2h−1} seem to be quite natural, and have been previously studied by the first named author. The present paper is devoted to the three choices G = G_2, Spin(7), Spin(9) of G-structures on S^m × S^{2h−1}, respectively with m + 2h − 1 = 7, 8, 16 and related with octonionic geometry.