Spinorial classification of Spin(7) structures

Martín‐Merchán, Lucía

doi:10.48550/arxiv.1803.08734

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2019

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“…More generally, the decomposition of the Spin(7)module Λ 5 ((R 8 ) * ) into irreducible submodules allows one to divide Spin(7)-structures into four classes, which were first described in [12]. Recently, a description of these classes in terms of spinorial equations has been obtained in [23].…”

Section: Introductionmentioning

confidence: 99%

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Homogeneous 8-manifolds admitting invariant Spin(7)-structures

Alekseevsky,

Chrysikos,

Fino

et al. 2019

Preprint

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We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connected. For each presentation, we exhibit explicit examples of invariant Spin( 7)-structures and we describe their type, according to Fernández classification. Finally, we analyse the associated Spin(7)-connection with torsion.

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Section: Introductionmentioning

confidence: 99%

“…Then, a direct computation shows that a basis of (Λ 2 V) H is given by e 12 − e 34 , e 13 + e 24 , e 14 − e 23 .…”

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confidence: 99%