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.
Parallelizations on products of spheres and octonionic geometry / Piccinni, Paolo. - In: COMPLEX MANIFOLDS. - ISSN 2300-7443. - 6:1(2019), pp. 138-149.
Parallelizations on products of spheres and octonionic geometry
Paolo Piccinni
2019
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 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.File allegati a questo prodotto
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