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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 Sharp map ： ウィキペディア英語版 Sharp map In differential geometry, the sharp map is the mapping that converts coordinate 1-forms into corresponding coordinate basis vectors. == Definition == Let $M$ be a manifold and $\backslash ,\backslash Gamma\; (TM)$ denote the space of all sections of its tangent bundle. Fix a nondegenerate (0,2)-tensor field $g\; \backslash in\; \backslash Gamma(T^$ *M^) , i.e., a metric tensor or a symplectic form. The definition :$X^\backslash flat\; :=\; i\_X\; g\; =\; g(X,.)$ yields a linear map sometimes called the flat map :$\backslash flat\; :\; \backslash Gamma(TM)\; \backslash to\; \backslash Gamma(T^$ *M) which is an isomorphism, since $g$ is non-degenerate. Its inverse :$\backslash sharp\; :=\; \backslash flat^\; :\; \backslash Gamma(T^$ *M) \to \Gamma(TM) is called the sharp map. 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「Sharp map」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.