Discrete Groups of Motions of Spaces of Constant Curvature
Discrete Groups of Motions of Spaces of Constant Curvature
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常曲率空间的离散运动群
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
O. Shvartsman
中科院分区：
文献类型：
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作者：
E. Vinberg;O. Shvartsman
常曲率空间运动的离散群，以及其他可以被视为常曲率空间运动的群（尽管它们可以被不同地定义），在数学及其应用的不同领域中自然出现。例子是对称群的正多面体，对称群的装饰和晶体结构，离散群的全纯变换所产生的一致化理论的黎曼曲面，基本群体的空间形式，群体的整数洛伦兹变换等（见第1章）。他们的研究在几何学发展史上写下了光辉的一页。
Discrete groups of motions of spaces of constant curvature, as well as other groups that can be regarded as such (although they may be defined differently), arise naturally in different areas of mathematics and its applications. Examples are the symmetry groups of regular polyhedra, symmetry groups of ornaments and crystallographic structures, discrete groups of holomorphic transformations arising in the uniformization theory of Riemannian surfaces, fundamental groups of space forms, groups of integer Lorentz transformations etc. (see Chapter 1). Their study fills a brilliant page in the development of geometry.