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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Flat vector bundle ： ウィキペディア英語版 Flat vector bundle In mathematics, a vector bundle is said to be ''flat'' if it is endowed with an linear connection with vanishing curvature, ''ie.'' a flat connection. ==de Rham cohomology of a flat vector bundle== Let $\backslash pi:E\; \backslash to\; X$ denote a flat vector bundle, and $\backslash nabla\; :\; \backslash Gamma(X,E)\backslash to\; \backslash Gamma(X,\; \backslash Omega\_X^1\backslash otimes\; E)$ be the covariant derivative associated to the flat connection on E. Let $\backslash Omega\_X^$ * (E) = \Omega^ *_X \otimes E denote the vector space (in fact a sheaf of modules over $\backslash mathcal\; O\_X$) of differential forms on ''X'' with values in ''E''. The covariant derivative defines a degree 1 endomorphism ''d'', the differential of $\backslash Omega\_X^$ * (E), and the flatness condition is equivalent to the property $d^2\; =\; 0$. In other words, the graded vector space $\backslash Omega\_X^$ * (E) is a cochain complex. Its cohomology is called the de Rham cohomology of ''E'', or de Rham cohomology with coefficients twisted by the local coefficient system ''E''. 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「Flat vector bundle」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.