$G_2$-Manifolds With Parallel Characteristic Torsion

Details $G_2$-Manifolds With Parallel Characteristic Torsion $G_2$-Manifolds With Parallel Characteristic Torsion

2006-04-20

arxiv.org/abs/math/0604441v1

Mathematics

Differential Geometry

19 pages

Scientific paper

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 $\Psi_1$ 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.

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