翻訳と辞書 Words near each other ・ Connection (album) ・ Connection (algebraic framework) ・ Connection (composite bundle) ・ Connection (dance) ・ Connection (Don Ellis album) ・ Connection (Elastica song) ・ Connection (EP) ・ Connection (fibred manifold) ・ Connection (mathematics) ・ Connection (principal bundle) ・ Connection (The Rolling Stones song) ・ Connection (vector bundle) ・ Connection broker ・ Connection Collection, Vol. 1 ・ Connection Distributing Co. v. Holder ・ Connection form ・ Connection game ・ Connection Lost ・ Connection Machine ・ Connection Magazines ・ Connection Pointe Christian Church of Brownsburg ・ Connection pool ・ Connection string ・ Connection-oriented communication ・ Connection-oriented Ethernet ・ Connectionism ・ Connectionist expert system ・ Connectionless communication ・ Connectionless routing ・ Connectionless-mode Network Service Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Connection form ： ウィキペディア英語版 Connection form 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.〔, , 〕 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. ==Vector bundles== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Connection form」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.