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Differential GeometryBundles, Connections, Metrics and Curvature$
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Clifford Henry Taubes

Print publication date: 2011

Print ISBN-13: 9780199605880

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199605880.001.0001

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Covariant derivatives and metrics

Covariant derivatives and metrics

(p.205) 15 Covariant derivatives and metrics
Differential Geometry

Clifford Henry Taubes

Oxford University Press

This chapter examines relations between covariant derivatives and metrics. It covers metric compatible covariant derivatives; torsion free covariant derivatives on T*M; the Levi-Civita connection/covariant derivative; a formula for the Levi-Civita connection; covariantly constant sections; an example of the Levi-Civita connection; and the curvature of the Levi-Civita connection.

Keywords:   covariant derivatives, metrics, tangent bundle, Levi-Civita connection

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