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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, connections and curvature

Covariant derivatives, connections and curvature

Chapter:
(p.139) 12 Covariant derivatives, connections and curvature
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0012

This chapter examines the notion of the curvature of a covariant derivative or connection. It begins by describing two notions involving differentiation of differential forms and vector fields that require no auxiliary choices. These are used to define curvature when covariant derivatives reappear in the story. It then explains the notion of curvature and gives an example. It also discusses curvature and commutators; connections and curvature; and the horizontal subbundle.

Keywords:   curvature, covariant derivative, connections, horizontal subbundle, commutators, vectors fields

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