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- Connection_form abstract "In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms.Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of frame, and so is not a tensorial object. Various generalizations and reinterpretations of the connection form were formulated subsequent to Cartan's initial work. In particular, on a principal bundle, a principal connection is a natural reinterpretation of the connection form as a tensorial object. On the other hand, the connection form has the advantage that it is a differential form defined on the differentiable manifold, rather than on an abstract principal bundle over it. Hence, despite their lack of tensoriality, connection forms continue to be used because of the relative ease of performing calculations with them.Griffiths & Harris (1978) Wells (1980) Spivak (1999) In physics, connection forms are also used broadly in the context of gauge theory, through the gauge covariant derivative.A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is not tensorial because under a change of basis, the connection form transforms in a manner that involves the exterior derivative of the transition functions, in much the same way as the Christoffel symbols for the Levi-Civita connection. The main tensorial invariant of a connection form is its curvature form. In the presence of a solder form identifying the vector bundle with the tangent bundle, there is an additional invariant: the torsion form. In many cases, connection forms are considered on vector bundles with additional structure: that of a fiber bundle with a structure group.".
- Connection_form wikiPageID "706412".
- Connection_form wikiPageRevisionID "597581319".
- Connection_form hasPhotoCollection Connection_form.
- Connection_form subject Category:Connection_(mathematics).
- Connection_form subject Category:Differential_geometry.
- Connection_form subject Category:Fiber_bundles.
- Connection_form type AnimalTissue105267548.
- Connection_form type BodyPart105220461.
- Connection_form type FiberBundle105475681.
- Connection_form type FiberBundles.
- Connection_form type NervousTissue105296775.
- Connection_form type Part109385911.
- Connection_form type PhysicalEntity100001930.
- Connection_form type Thing100002452.
- Connection_form type Tissue105267345.
- Connection_form comment "In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms.Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of frame, and so is not a tensorial object.".
- Connection_form label "Connection form".
- Connection_form label "接続形式".
- Connection_form label "联络形式".
- Connection_form sameAs 接続形式.
- Connection_form sameAs m.034db8.
- Connection_form sameAs Q5161687.
- Connection_form sameAs Q5161687.
- Connection_form sameAs Connection_form.
- Connection_form wasDerivedFrom Connection_form?oldid=597581319.
- Connection_form isPrimaryTopicOf Connection_form.