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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 Symplectic frame bundle ： ウィキペディア英語版 Symplectic frame bundle In symplectic geometry, the symplectic frame bundle〔 〕 of a given symplectic manifold $(M,\; \backslash omega)\backslash ,$ is the canonical principal $)$-subbundle $\backslash pi\_\backslash colon\backslash to\; M\backslash ,$ of the tangent frame bundle $\backslash mathrm\; FM\backslash ,$ consisting of linear frames which are symplectic with respect to $\backslash omega\backslash ,$. In other words, an element of the symplectic frame bundle is a linear frame $u\backslash in\backslash mathrm\_(M)\backslash ,$ at point $p\backslash in\; M\backslash ,\; ,$ i.e. an ordered basis $(\_1,\backslash dots,\_n,\_1,\backslash dots,\_n)\backslash ,$ of tangent vectors at $p\backslash ,$ of the tangent vector space $T\_(M)\backslash ,$, satisfying :$\backslash omega\_(\_j,\_k)=\backslash omega\_(\_j,\_k)=0\backslash ,$ and $\backslash omega\_(\_j,\_k)=\backslash delta\_\backslash ,$ for $j,k=1,\backslash dots,n\backslash ,$. For $p\backslash in\; M\backslash ,$, each fiber $\_p\backslash ,$ of the principal $)$-bundle $\backslash pi\_\backslash colon\backslash to\; M\backslash ,$ is the set of all symplectic bases of $T\_(M)\backslash ,$. The symplectic frame bundle $\backslash pi\_\backslash colon\backslash to\; M\backslash ,$, a subbundle of the tangent frame bundle $\backslash mathrm\; FM\backslash ,$, is an example of reductive G-structure on the manifold $M\backslash ,$. ==See also== * Metaplectic group * Metaplectic structure * Symplectic basis * Symplectic structure * Symplectic geometry * Symplectic group * Symplectic spinor bundle 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「Symplectic frame 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.