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 spin(7) spin(9) octonions parallelizations on spheres locally conformally parallel primary 53c26 53c27 53c35 57r25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ddca1e222d384027b5122b50db3c592c
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spelling	oai:doaj.org-article:ddca1e222d384027b5122b50db3c592c2021-12-02T19:08:48ZParallelizations on products of spheres and octonionic geometry2300-744310.1515/coma-2019-0007https://doaj.org/article/ddca1e222d384027b5122b50db3c592c2019-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2019-0007https://doaj.org/toc/2300-7443A 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.Parton MaurizioPiccinni PaoloDe Gruyterarticleg2spin(7)spin(9)octonionsparallelizations on sphereslocally conformally parallelprimary 53c2653c2753c3557r25MathematicsQA1-939ENComplex Manifolds, Vol 6, Iss 1, Pp 138-149 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	g2 spin(7) spin(9) octonions parallelizations on spheres locally conformally parallel primary 53c26 53c27 53c35 57r25 Mathematics QA1-939
spellingShingle	g2 spin(7) spin(9) octonions parallelizations on spheres locally conformally parallel primary 53c26 53c27 53c35 57r25 Mathematics QA1-939 Parton Maurizio Piccinni Paolo Parallelizations on products of spheres and octonionic geometry
description	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.
format	article
author	Parton Maurizio Piccinni Paolo
author_facet	Parton Maurizio Piccinni Paolo
author_sort	Parton Maurizio
title	Parallelizations on products of spheres and octonionic geometry
title_short	Parallelizations on products of spheres and octonionic geometry
title_full	Parallelizations on products of spheres and octonionic geometry
title_fullStr	Parallelizations on products of spheres and octonionic geometry
title_full_unstemmed	Parallelizations on products of spheres and octonionic geometry
title_sort	parallelizations on products of spheres and octonionic geometry
publisher	De Gruyter
publishDate	2019
url	https://doaj.org/article/ddca1e222d384027b5122b50db3c592c
work_keys_str_mv	AT partonmaurizio parallelizationsonproductsofspheresandoctonionicgeometry AT piccinnipaolo parallelizationsonproductsofspheresandoctonionicgeometry
_version_	1718377180501639168

Parallelizations on products of spheres and octonionic geometry

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