About: Exterior covariant derivative

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In the mathematical field of differential geometry, the exterior covariant derivative is an extension of the notion of exterior derivative to the setting of a differentiable principal bundle or vector bundle with a connection.

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rdfs:label	Exterior covariant derivative (en) 外共变导数 (zh)
rdfs:comment	In the mathematical field of differential geometry, the exterior covariant derivative is an extension of the notion of exterior derivative to the setting of a differentiable principal bundle or vector bundle with a connection. (en) 在数学中，外共变导数（exterior covariant derivative），时或称为共变外导数（covariant exterior derivative），是中一个非常有用的概念，它可能将利用主联络的公式化简。设 P → M 是光滑流形 M 上一个主 G-丛。如果是 P 上一个张量性 k-形式，则其外共变导数定义为：这里 h 表示到水平子空间的投影，由联络定义，其核为该纤维丛的切丛的（铅直子空间）。这里是 P 上任何向量场。Dφ 是 P 上一个张量性 k+1 形式。不像通常的外导数的平方是 0，我们有这里表示曲率形式。特别的对消没。 (zh)
rdfs:seeAlso	Second covariant derivative
dcterms:subject	Differential geometry Connection (mathematics) Fiber bundles
Wikipage page ID	849738 (xsd:integer)
Wikipage revision ID	1119101218 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press American Journal of Mathematics Princeton University Press Electromagnetism Representation of a Lie group Curvature form Lie algebra-valued differential form Differential geometry Mathematics Connection (principal bundle) Connection (vector bundle) Springer Publishing Exterior derivative Oxford University Press Equivariant Abuse of notation Connection (mathematics) Fiber bundles Differential geometry Associated bundle Springer, Cham Lie bracket of vector fields Smooth manifold Vector bundle Principal bundle Tensorial form John Wiley & Sons, Inc. Physics Reports Inverse matrix Vector-valued differential forms Vector-valued form Springer-Verlag Bianchi's second identity North-Holland Publishing Company Field strength tensor Flat connection Connection one-form Vertical subspace Horizontal subspace
Link from a Wikipage to an external page	https://www.emis.de/monographs/KSM/
sameAs	Exterior covariant derivative Exterior covariant derivative Exterior covariant derivative Exterior covariant derivative Exterior covariant derivative
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4a	Taylor (en)
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1a	Donaldson (en) Sampson (en) Kolář (en) Slovák (en) Besse (en) Eells (en) Milnor (en) Kronheimer (en) Michor (en) Stasheff (en)
1loc	Section 1.12 (en) Section 3.A.3 (en)
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1y	1964 (xsd:integer) 1974 (xsd:integer) 1987 (xsd:integer)

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