When is a Connection a Levi-Civita Connection?
Differential Geometry
2008-04-18 v1
Abstract
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.
Cite
@article{arxiv.0804.2698,
title = {When is a Connection a Levi-Civita Connection?},
author = {Richard Atkins},
journal= {arXiv preprint arXiv:0804.2698},
year = {2008}
}
Comments
30 pages