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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

Chapter:
(p.125) 11 Covariant derivatives and connections
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0011

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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