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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 Almost flat manifold ： ウィキペディア英語版 Almost flat manifold In mathematics, a smooth compact manifold ''M'' is called almost flat if for any $\backslash varepsilon>0$ there is a Riemannian metric $g\_\backslash varepsilon$ on ''M'' such that $\backslash mbox(M,g\_\backslash varepsilon)\backslash le\; 1$ and $g\_\backslash varepsilon$ is $\backslash varepsilon$-flat, i.e. for the sectional curvature of $K\_$ we have . In fact, given ''n'', there is a positive number $\backslash varepsilon\_n>0$ such that if a ''n''-dimensional manifold admits an $\backslash varepsilon\_n$-flat metric with diameter $\backslash le\; 1$ then it is almost flat. On the other hand one can fix the bound of sectional curvature and get the diameter going to zero, so the almost flat manifold is a special case of a collapsing manifold, which is collapsing along all directions. According to the Gromov—Ruh theorem, ''M'' is almost flat if and only if it is infranil. In particular, it is a finite factor of a nilmanifold, which is the total space of a principal torus bundle over a principal torus bundle over a torus. ==References== *. *. 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「Almost flat manifold」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.