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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 connections

Covariant derivatives and connections

(p.125) 11 Covariant derivatives and connections
Differential Geometry

Clifford Henry Taubes

Oxford University Press

This chapter examines the related notions of covariant derivative and connection. It covers the space of covariant derivatives. It also gives a relatively straightforward construction of a covariant derivative on a given vector bundle E → M with fiber 𝕍n = ℝnRn or ℂn. It looks at principal bundles and connections; connections and covariant derivatives; and horizontal lifts. The chapter gives an application to the classification of principal G-bundles up to isomorphism and explains connections, covariant derivatives, and pull-back bundles.

Keywords:   vector bundle, principal bundles, horizontal lifts, G-bundles, isomorphism, pull-back bundles

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