When is a Connection a Metric Connection?


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New Zealand Journal of Mathematics

Vol. 38, (2008), Pages 225-238

Richard Atkins

Trinity Western University

7600 Glover Road

Langley, BC, V2Y 1Y1



Abstract There are two sides 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. The local problem has been previously solved by means of constructing a derived flag. Herein we continue the inquiry to the global aspect, which is formulated in terms of the cohomology of the constant sheaf of sections in the general linear group.

Keywords regular connection, analytic connection, global parallel metric

Classification (MSC2000) 53C07

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