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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

Chapter:
(p.205) 15 Covariant derivatives and metrics
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0015

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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