2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64066We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a $\Spin(7)$-structure play a special role. Any geometry of that type admits a unique connection with totally skew-symmetric torsion. Under weak conditions on the structure group we prove that this geometry is the only one with this property. Finally, we discuss the automorphism group of a Riemannian manifold with a fixed non-integrable $\mathrm{G}$-structure.Latex2.09, 12 pagesDifferential GeometryHigh Energy Physics - Theory53C25, 81T30text