2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159026We consider the more general question as to when a connection is a metric connection. There are two aspects to this investigation: first, the determination of the integrability conditions that ensure the existence of a local parallel metric in the neighbourhood of a given point and second, the characterization of the topological obstruction to a globally defined parallel metric.30 pagesDifferential Geometrytext