2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61875A discussion of torsion of Riemannian G-structures leads to a survey of contributions of Alfred Gray and others on almost Hermitian manifolds, G_2-manifolds, curvature identities, volume expansions, plotting geodesics, and the geometry of nilmanifolds. The paper concludes with a new example of a compact 8-manifold with a quaternionic 4-form that is closed but not parallel.Proceedings, Congress in memory of Alfred Gray, to appear in AMS Contemporary MathematicsDifferential Geometry53C25text