When is a Connection a Levi-Civita Connection?

2008/04/16 by Richard Atkins, Atkins, Richard
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.0804.2698

30 pages

arxiv created 2008/04/16 · arxiv updated 2009/12/01

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.

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