%0 Journal Article
%T When is a Connection a Levi-Civita Connection?
%A Richard Atkins
%J Mathematics
%D 2008
%I arXiv
%X We 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.
%U http://arxiv.org/abs/0804.2698v1