翻訳と辞書 Words near each other ・ Space Flight Award ・ Space Flight Europe-America 500 ・ Space Flight Operations Facility ・ Space flight participant ・ Space flight simulator game ・ Space Florida ・ Space Flyer Unit ・ Space food ・ Space Food Sticks ・ Space for Life ・ Space for Pan African Research Creation and Knowledge ・ Space Force ・ Space force ・ Space Force (Action Force) ・ Space Force (disambiguation) ・ Space form ・ Space Foundation ・ Space fountain ・ Space frame ・ Space Frontier Foundation ・ Space Fury ・ Space Game ・ Space Games ・ Space Generation Advisory Council ・ Space geostrategy ・ Space Ghost ・ Space Ghost (TV series) ・ Space Ghost Coast to Coast ・ Space Ghost Coast to Coast (album) ・ Space Ghost's Musical Bar-B-Que 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 Space form ： ウィキペディア英語版 Space form In mathematics, a space form is a complete Riemannian manifold ''M'' of constant sectional curvature ''K''. The three obvious examples are Euclidean ''n''-space, the ''n''-dimensional sphere, and hyperbolic space, although a space form need not be simply connected. ==Reduction to generalized crystallography== The Killing–Hopf theorem of Riemannian geometry states that the universal cover of an ''n''-dimensional space form $M^n$ with curvature $K\; =\; -1$ is isometric to $H^n$, hyperbolic space, with curvature $K\; =\; 0$ is isometric to $R^n$, Euclidean ''n''-space, and with curvature $K\; =\; +1$ is isometric to $S^n$, the n-dimensional sphere of points distance 1 from the origin in $R^$. By rescaling the Riemannian metric on $H^n$, we may create a space $M\_K$ of constant curvature $K$ for any . Similarly, by rescaling the Riemannian metric on $S^n$, we may create a space $M\_K$ of constant curvature $K$ for any $K\; >\; 0$. Thus the universal cover of a space form $M$ with constant curvature $K$ is isometric to $M\_K$. This reduces the problem of studying space form to studying discrete groups of isometries $\backslash Gamma$ of $M\_K$ which act properly discontinuously. Note that the fundamental group of $M$, $\backslash pi\_1(M)$, will be isomorphic to $\backslash Gamma$. Groups acting in this manner on $R^n$ are called crystallographic groups. Groups acting in this manner on $H^2$ and $H^3$ are called Fuchsian groups and Kleinian groups, respectively. 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「Space form」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.