翻訳と辞書 Words near each other ・ Congrier ・ Congrinae ・ Congriscus ・ Congriscus maldivensis ・ Congriscus marquesaensis ・ Congriscus megastomus ・ Congro Volcanic Fissural System ・ Congrogadus subducens ・ Congrosoma evermanni ・ Congrove Field and The Tumps ・ Congrua ・ Congrua portio ・ Congruence ・ Congruence (general relativity) ・ Congruence (geometry) ・ Congruence (manifolds) ・ Congruence bias ・ Congruence coefficient ・ Congruence ideal ・ Congruence lattice problem ・ Congruence of squares ・ Congruence of triangles ・ Congruence principle ・ Congruence relation ・ Congruence subgroup ・ Congruence-permutable algebra ・ Congruent isoscelizers point ・ Congruent melting ・ Congruent number ・ Congruent transformation 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 Congruence (manifolds) ： ウィキペディア英語版 Congruence (manifolds) In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold. Congruences are an important concept in general relativity, and are also important in parts of Riemannian geometry. ==A motivational example== The idea of a congruence is probably better explained by giving an example than by a definition. Consider the smooth manifold R². Vector fields can be specified as ''first order linear partial differential operators'', such as :$\backslash vec\; =\; (\; x^2\; -\; y^2\; )\; \backslash ,\; \backslash partial\_x\; +\; 2\; \backslash ,\; x\; y\; \backslash ,\; \backslash partial\_y$ These correspond to a system of ''first order linear ordinary differential equations'', in this case :$\backslash dot\; =\; x^2\; -\; y^2,\backslash ;\; \backslash dot\; =\; 2\; \backslash ,\; x\; y$ where dot denotes a derivative with respect to some (dummy) parameter. The solutions of such systems are ''families of parameterized curves'', in this case :$x(\backslash lambda)\; =\; \backslash frac$ :$y(\backslash lambda)\; =\; \backslash frac$ This family is what is often called a ''congruence of curves'', or just ''congruence'' for short. This particular example happens to have two ''singularities'', where the vector field vanishes. These are fixed points of the ''flow''. (A flow is a one-dimensional group of diffeomorphisms; a flow defines an action by the one-dimensional Lie group R, having locally nice geometric properties.) These two singularities correspond to two ''points'', rather than two curves. In this example, the other integral curves are all simple closed curves. Many flows are considerably more complicated than this. To avoid complications arising from the presence of singularities, usually one requires the vector field to be ''nonvanishing''. If we add more mathematical structure, our congruence may acquire new significance. 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「Congruence (manifolds)」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.