Parallelizations on products of spheres and octonionic geometry

Abstract

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.

Keywords

• g2
• spin(7)
• spin(9)
• octonions
• parallelizations on spheres
• locally conformally parallel
• primary 53c26
• 53c27
• 53c35
• 57r25