$G_2$-Manifolds With Parallel Characteristic Torsion

Abstract

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.

19 pages

References in corpus (1)

• On types of non-integrable geometries

Cited by in corpus (2)

• Curvature decomposition of G_2 manifolds
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5