Parallelizations on products of spheres and octonionic geometry

IF 0.5 Q3 MATHEMATICS Complex Manifolds Pub Date : 2019-01-01 DOI:10.1515/coma-2019-0007

M. Parton, P. Piccinni

引用次数: 1

Abstract

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.

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球面与八次几何乘积的并行化

一个经典的Kervaire定理指出，球的积当且仅当至少一个因子具有奇维数时是可并行的。Sm × S2h−1上的两个显式并行似乎是很自然的，并且在[32]中已经被第一作者研究过。本文讨论了Sm × S2h−1上G-结构在m + 2h−1 = 7,8,16时的三种选择G = G2, Spin(7)， Spin(9)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.

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