$G_2$-Manifolds With Parallel Characteristic Torsion

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We classify 7-dimensional cocalibrated $\G_2$-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection $\nabla^{\mathrm{c}}$ with totally skew-symmetric torsion and a spinor field $Ψ_1$ solving the equations in the common sector of type II superstring theory. There exist $\G_2$-structures with parallel characteristic torsion that are not naturally reductive.
19 pages

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Differential Geometry, 53C25; 81T30

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http://salesiana.dossiersoluciones.com/handle/123456789/111636

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604441
 http://arxiv.org/abs/math/0604441

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arXiv