English

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

R2 v1 2026-06-21T10:31:49.826Z