The Classification of Non-Euclidean Plane Crystallographic Groups
The Classification of Non-Euclidean Plane Crystallographic Groups
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非欧几里得平面晶族的分类
DOI：
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发表时间：
1967
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通讯作者：
A. Macbeath
中科院分区：
文献类型：
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作者：
A. Macbeath
本文研究了商空间为紧空间的非欧平面晶体群（简称NEC群）的代数分类。考虑的群体是离散组的运动的Lobatschewsky或双曲平面，包括那些包含方向反转反射和滑翔反射。Fuchsian群的相应问题，只包含可定向变换，基本上是解决了在工作中的Rebecke和克莱因（6）。
This paper deals with the algebraic classification of non-euclidean plane crystallographic groups (NEC groups, for short) with compact quotient space. The groups considered are the discrete groups of motions of the Lobatschewsky or hyperbolic plane, including those which contain orientation-reversing reflections and glide-reflections. The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Fricke and Klein (6).