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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 affine bundle ： ウィキペディア英語版 affine bundle In mathematics, an affine bundle is a fiber bundle whose typical fiber, fibers, trivialization morphisms and transition functions are affine.〔. (page 60)〕 ==Formal definition== Let $\backslash overline\backslash pi:\backslash overline\; Y\backslash to\; X$ be a vector bundle with a typical fiber a vector space $\backslash overline\; F$. An affine bundle modelled on a vector bundle $\backslash overline\backslash pi:\backslash overline\; Y\backslash to\; X$ is a fiber bundle $\backslash pi:Y\backslash to\; X$ whose typical fiber $F$ is an affine space modelled on $\backslash overline\; F$ so that the following conditions hold: (i) All the fiber $Y\_x$ of $Y$ are affine spaces modelled over the corresponding fibers $\backslash overline\; Y\_x$ of a vector bundle $\backslash overline\; Y$. (ii) There is an affine bundle atlas of $Y\backslash to\; X$ whose local trivializations morphisms and transition functions are affine isomorphisms. Dealing with affine bundles, one uses only affine bundle coordinates $(x^\backslash mu,y^i)$ possessing affine transition functions : $y\text{'}^i=\; A^i\_j(x^\backslash nu)y^j\; +\; b^i(x^\backslash nu).$ There are the bundle morphisms : $Y\backslash times\_X\backslash overline\; Y\backslash longrightarrow\; Y,\backslash qquad\; (y^i,\; \backslash overline\; y^i)\backslash longmapsto\; y^i\; +\backslash overline\; y^i,$ :$Y\backslash times\_X\; Y\backslash longrightarrow\; \backslash overline\; Y,\backslash qquad\; (y^i,\; y\text{'}^i)\backslash longmapsto\; y^i\; -\; y\text{'}^i,$ where $(\backslash overline\; y^i)$ are linear bundle coordinates on a vector bundle $\backslash overline\; Y$, possessing linear transition functions $\backslash overline\; y\text{'}^i=\; A^i\_j(x^\backslash nu)\backslash overline\; y^j$. 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「affine 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.