翻訳と辞書 Words near each other ・ Metro 2 Radio ・ Metro 2033 ・ Metro 2033 (disambiguation) ・ Metro 2033 (video game) ・ Metro 2034 ・ Metro 2035 ・ Metro 21 ・ Metro 3 ・ Metric (band) ・ Metric (mathematics) ・ Metric (unit) ・ Metric (vector bundle) ・ Metric Act of 1866 ・ Metric Arts ・ Metric Commission ・ Metric connection ・ Metric conversion ・ Metric Conversion Act ・ Metric derivative ・ Metric differential ・ Metric dimension ・ Metric dimension (graph theory) ・ Metric discography ・ Metric engine (American expression) ・ Metric expansion of space ・ Metric foot ・ Metric gauge ・ Metric Hosiery Company ・ Metric k-center ・ Metric map Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Metric connection ： ウィキペディア英語版 Metric connection In mathematics, a metric connection is a connection in a vector bundle ''E'' equipped with a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. Other common equivalent formulations of a metric connection include: * A connection for which the covariant derivatives of the metric on ''E'' vanish. * A principal connection on the bundle of orthonormal frames of ''E''. A special case of a metric connection is the Levi-Civita connection. Here the bundle ''E'' is the tangent bundle of a manifold. In addition to being a metric connection, the Levi-Civita connection is required to be torsion free. ==Riemannian connections== An important special case of a metric connection is a Riemannian connection. This is a connection $\backslash nabla$ on the tangent bundle of a pseudo-Riemannian manifold (''M'', ''g'') such that $\backslash nabla\_X\; g\; =\; 0$ for all vector fields ''X'' on ''M''. Equivalently, $\backslash nabla$ is Riemannian if the parallel transport it defines preserves the metric ''g''. A given connection $\backslash nabla$ is Riemannian if and only if :$Xg(Y,Z)=g(\backslash nabla\_XY,Z)+g(Y,\backslash nabla\_XZ)$ for all vector fields ''X'', ''Y'' and ''Z'' on ''M'', where $Xg(Y,Z)$ denotes the derivative of the function $g(Y,Z)$ along this vector field $X$. The Levi-Civita connection is the torsion-free Riemannian connection on a manifold. It is unique by the fundamental theorem of Riemannian geometry. 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「Metric connection」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.