翻訳と辞書 Words near each other ・ Isometrus khammamensis ・ Isometrus krasenskyi ・ Isometrus kurkai ・ Isometrus loebli ・ Isometrus maculatus ・ Isometrus navaiae ・ Isometrus petrzelkai ・ Isometrus problematicus ・ Isometrus rigidulus ・ Isometrus thurstoni ・ Isometrus thwaitesi ・ Isometrus vittatus ・ Isometrus zideki ・ Isometry ・ Isometry (disambiguation) ・ Isometry (Riemannian geometry) ・ Isometry group ・ Isomigrastatin ・ IsomiR ・ Isomira ・ Isomma ・ Isomma hieroglyphicum ・ Isomonodromic deformation ・ Isomoralla eriscota ・ Isomorph ・ Isomorph Records ・ Isomorphic keyboard ・ Isomorphism ・ Isomorphism (biology) ・ Isomorphism (crystallography) 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 Isometry (Riemannian geometry) ： ウィキペディア英語版 Isometry (Riemannian geometry) In the study of Riemannian geometry in mathematics, a local isometry from one (pseudo-)Riemannian manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a diffeomorphism, such a map is called an isometry (or isometric isomorphism), and provides a notion of isomorphism ("sameness") in the category Rm of Riemannian manifolds. ==Definition== Let $(M,\; g)$ and $(M\text{'},\; g\text{'})$ be two (pseudo-)Riemannian manifolds, and let $f\; :\; M\; \backslash to\; M\text{'}$ be a diffeomorphism. Then $f$ is called an isometry (or isometric isomorphism) if :$g\; =\; f^\; g\text{'},\; \backslash ,$ where $f^\; g\text{'}$ denotes the pullback of the rank (0, 2) metric tensor $g\text{'}$ by $f$. Equivalently, in terms of the push-forward $f\_$, we have that for any two vector fields $v,\; w$ on $M$ (i.e. sections of the tangent bundle $\backslash mathrm\; M$), :$g(v,\; w)\; =\; g\text{'}\; \backslash left(\; f\_\; v,\; f\_\; w\; \backslash right).\; \backslash ,$ If $f$ is a local diffeomorphism such that $g\; =\; f^\; g\text{'}$, then $f$ is called a local isometry. 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「Isometry (Riemannian geometry)」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.