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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 Fuchsian model ： ウィキペディア英語版 Fuchsian model In mathematics, a Fuchsian model is a construction of a hyperbolic Riemann surface ''R'' as a quotient of the upper half-plane H. By the uniformization theorem, every Riemann surface is either elliptic, parabolic or hyperbolic. Every hyperbolic Riemann surface has a non-trivial fundamental group $\backslash pi\_1(R)$. The fundamental group can be shown to be isomorphic to some subgroup Γ of the group of real Möbius transformations $SL(2,\backslash mathbb)$, this subgroup being a Fuchsian group. The quotient space H/Γ is then a Fuchsian model for the Riemann surface ''R''. Many authors use the terms ''Fuchsian group'' and ''Fuchsian model'' interchangeably, letting the one stand for the other. The latter remark is true mostly of the creator of this page. Meanwhile, Matsuzaki reserves the term Fuchsian model for the Fuchsian group, never the surface itself. ==A more precise definition== To be more precise, every Riemann surface has a universal covering map that is either the Riemann sphere, the complex plane or the upper half-plane. Given a covering map $f:\backslash mathbb\backslash rightarrow\; R$, where H is the upper half-plane. The Fuchsian model of ''R'' is the quotient space $R^h\; =\; \backslash mathbb\; /\; \backslash Gamma$. ''R''. Note that $R^h$ is a complete 2D hyperbolic manifold. 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「Fuchsian model」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.