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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 Kosmann lift ： ウィキペディア英語版 Kosmann lift In differential geometry, the Kosmann lift,〔Fatibene L., Ferraris M., Francaviglia M. and Godina M. (1996), ''A geometric definition of Lie derivative for Spinor Fields'', in: Proceedings of the ''6th International Conference on Differential Geometry and Applications,'' August 28th–September 1st 1995 (Brno, Czech Republic), Janyska J., Kolář I. & J. Slovák J. (Eds.), Masaryk University, Brno, pp. 549–558〕〔Godina M. and Matteucci P. (2003), ''Reductive G-structures and Lie derivatives'', Journal of Geometry and Physics 47, 66–86〕〔Fatibene L. and Francaviglia M. (2011), ''General theory of Lie derivatives for Lorentz tensors'', Communications in Mathematics 19, 11–25〕 named after Yvette Kosmann-Schwarzbach, of a vector field $X\backslash ,$ on a Riemannian manifold $(M,g)\backslash ,$ is the canonical projection $X\_\backslash ,$ on the orthonormal frame bundle of its natural lift $\backslash hat\backslash ,$ defined on the bundle of linear frames.〔 (''Example'' 5.2) pp. 55-56〕 Generalisations exist for any given reductive G-structure. ==Introduction== In general, given a subbundle $Q\backslash subset\; E\backslash ,$ of a fiber bundle $\backslash pi\_\backslash colon\; E\backslash to\; M\backslash ,$ over $M$ and a vector field $Z\backslash ,$ on $E$, its restriction $Z\backslash vert\_Q\backslash ,$ to $Q$ is a vector field "along" $Q$ not ''on'' (i.e., ''tangent'' to) $Q$. If one denotes by $i\_\; \backslash colon\; Q\backslash hookrightarrow\; E$ the canonical embedding, then $Z\backslash vert\_Q\backslash ,$ is a section of the pullback bundle $i^\_(TE)\; \backslash to\; Q\backslash ,$, where :$i^\_(TE)\; =\; \backslash \backslash subset\; Q\backslash times\; TE,\backslash ,$ and $\backslash tau\_\backslash colon\; TE\backslash to\; E\backslash ,$ is the tangent bundle of the fiber bundle $E$. Let us assume that we are given a Kosmann decomposition of the pullback bundle $i^\_(TE)\; \backslash to\; Q\backslash ,$, such that :$i^\_(TE)\; =\; TQ\backslash oplus\; \backslash mathcal\; M(Q),\backslash ,$ i.e., at each $q\backslash in\; Q$ one has $T\_qE=T\_qQ\backslash oplus\; \backslash mathcal\; M\_u\backslash ,,$ where $\backslash mathcal\; M\_$ is a vector subspace of $T\_qE\backslash ,$ and we assume $\backslash mathcal\; M(Q)\backslash to\; Q\backslash ,$ to be a vector bundle over $Q$, called the transversal bundle of the Kosmann decomposition. It follows that the restriction $Z\backslash vert\_Q\backslash ,$ to $Q$ splits into a ''tangent'' vector field $Z\_K\backslash ,$ on $Q$ and a ''transverse'' vector field $Z\_G,\backslash ,$ being a section of the vector bundle $\backslash mathcal\; M(Q)\backslash to\; Q.\backslash ,$ 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「Kosmann lift」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.