ON VOLUMES OF NON-EUCLIDEAN POLYTOPES
ON VOLUMES OF NON-EUCLIDEAN POLYTOPES
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关于非欧多面体的体积
DOI：
10.1007/978-94-011-0924-6_10
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Ruth Kellerhals
中科院分区：
文献类型：
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作者：
Ruth Kellerhals
罗巴切夫斯基和施莱弗里已经研究过计算非欧多面体的体积的问题，这一问题具有实际意义，特别是与双曲空间形式的体积谱结构有关。这些结果的简要总结和双曲多面体的体积问题的介绍。一些双曲五维流形的covolums计算，这些是建立在简单的组合度量型双曲晶体，它们的体积都可与黎曼的zeta函数在3。
The problem of calculating volumes of non-Euclidean polytopes was already studied by Lobachevsky and Schläfli and is of actual interest, in particular, in connection with the structure of volume spectra of hyperbolic space forms. A brief summary of these results and an introduction to the volume problem for hyperbolic polytopes are given. The covolumes of some hyperbolic five-dimensional manifolds are computed; these are built upon hyperbolic crystals of simple combinatorial metrical type, and their volumes are all commensurable with Riemann’s zeta function at three.