2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111636We 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 pagesDifferential Geometry53C25; 81T30text