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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 Campbell's theorem (geometry) ： ウィキペディア英語版 Campbell's theorem (geometry) Campbell's theorem, also known as Campbell’s embedding theorem and the Campbell-Magaarrd theorem, is a mathematical theorem that evaluates the asymptotic distribution of random impulses acting with a determined intensity on a damped system. The theorem guarantees that any n-dimensional Riemannian manifold can be locally embedded in an (''n'' + 1)-dimensional Ricci-flat Riemannian manifold.〔Romero, Carlos, Reza Tavakol, and Roustam Zalaltedinov. ''The Embedding of General Relativity in Five Dimensions''. N.p.: Springer Netherlands, 2005.〕 ==Statement== Campbell's theorem states that any ''n''-dimensional Riemannian manifold can be embedded locally in an (''n'' + 1)-manifold with a Ricci curvature of ''R''a'' ''b'' = 0. The theorem also states, in similar form, that an ''n''-dimensional pseudo-Riemannian manifold can be both locally and isometrically embedded in an ''n''(''n'' + 1)/2-pseudo-Euclidean space. 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「Campbell's theorem (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.