2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190835We describe all almost contact metric, almost hermitian and $G_2$-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the $\nabla$-parallel spinors. In particular, we obtain solutions of the type II string in dimension $n=5,6$ and 7.Latex2e, 35 pagesDifferential GeometryHigh Energy Physics - Theory53C25, 53C27, 53C55, 81T30text