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词汇 Uniformization theorem
分类 英语词汇 英语翻译词典
释义

Uniformization theorem

中文百科

单值化定理

数学上,曲面的单值化定理是说任何曲面上都有一个常高斯曲率的度量。事实上,在每一个给定的共形类中我们都可以找到一个常高斯曲率的度量。等价的说,用复分析的语言,任何单连通的黎曼曲面都共形等价于复平面、单位圆盘和黎曼球面三者之一。

英语百科

Uniformization theorem 单值化定理

In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of the three domains: the open unit disk, the complex plane, or the Riemann sphere. In particular it admits a Riemannian metric of constant curvature. This classifies Riemannian surfaces as elliptic (positively curved – rather, admitting a constant positively curved metric), parabolic (flat), and hyperbolic (negatively curved) according to their universal cover.

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