翻訳と辞書 Words near each other ・ Hypercompe ochreator ・ Hypercompe ockendeni ・ Hypercompe ocularia ・ Hypercompe orbiculata ・ Hypercompe orsa ・ Hypercompe oslari ・ Hypercompe permaculata ・ Hypercompe perplexa ・ Hypercompe persephone ・ Hypercompe persola ・ Hypercompe pertestacea ・ Hypercompe peruvensis ・ Hypercompe praeclara ・ Hyperbolic law of cosines ・ Hyperbolic link ・ Hyperbolic manifold ・ Hyperbolic motion ・ Hyperbolic motion (relativity) ・ Hyperbolic navigation ・ Hyperbolic orthogonality ・ Hyperbolic partial differential equation ・ Hyperbolic plane (disambiguation) ・ Hyperbolic point ・ Hyperbolic quaternion ・ Hyperbolic secant distribution ・ Hyperbolic sector ・ Hyperbolic set ・ Hyperbolic space ・ Hyperbolic spiral ・ Hyperbolic structure 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 Hyperbolic manifold ： ウィキペディア英語版 Hyperbolic manifold In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in dimensions 2 and 3, where they are called hyperbolic surfaces and hyperbolic 3-manifolds, respectively. In these dimensions, they are important because most manifolds can be made into a hyperbolic manifold by a homeomorphism. This is a consequence of the uniformization theorem for surfaces and the geometrization theorem for 3-manifolds proved by Perelman. ==Rigorous Definition== A hyperbolic $n$-manifold is a complete Riemannian n-manifold of constant sectional curvature -1. Every complete, connected, simply-connected manifold of constant negative curvature −1 is isometric to the real hyperbolic space $\backslash mathbb^n$. As a result, the universal cover of any closed manifold M of constant negative curvature −1 is $\backslash mathbb^n$. Thus, every such M can be written as $\backslash mathbb^n/\backslash Gamma$ where Γ is a torsion-free discrete group of isometries on $\backslash mathbb^n$. That is, Γ is a discrete subgroup of $SO^+\_\backslash mathbb$. The manifold has finite volume if and only if Γ is a lattice. Its thick-thin decomposition has a thin part consisting of tubular neighborhoods of closed geodesics and ends which are the product of a Euclidean ''n-1''-manifold and the closed half-ray. The manifold is of finite volume if and only if its thick part is compact. For n>2 the hyperbolic structure on a ''finite volume'' hyperbolic ''n''-manifold is unique by Mostow rigidity and so geometric invariants are in fact topological invariants. 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「Hyperbolic 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.