Parallelizations on products of spheres and octonionic geometry

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...

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Autores principales: Parton Maurizio, Piccinni Paolo
Formato: article
Lenguaje:EN
Publicado: De Gruyter 2019
Materias:
g2
Acceso en línea:https://doaj.org/article/ddca1e222d384027b5122b50db3c592c
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Sumario: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.