2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161353Let (M,I,J,K) be a compact hypercomplex manifold admitting an HKT-metric. Assume that the canonical bundle of (M,I) is trivial as a holomorphic line bundle. We show that the holonomy of Obata connection on M is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds equipped with abelian hypercomplex structures, showing that such manifolds have holonomy in SL(n,H).14 pages, minor misprints correctedDifferential GeometryAlgebraic Geometrytext