On right-angled reflection groups in hyperbolic spaces
On right-angled reflection groups in hyperbolic spaces
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DOI：
10.4171/cmh/4
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发表时间：
2005-03
影响因子：
0.9
通讯作者：
L. Potyagailo;E. Vinberg
中科院分区：
文献类型：
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作者：
L. Potyagailo;E. Vinberg
证明了双曲空间$\Bbb H ^n $中有限体积的直角双曲多面体仅当n\leq 14.$我们还提供了一类维数为n = 3，4，.的多面体，八美元。我们证明了对于$n = 3，4 $，这个族的成员在所有相应维数的双曲直角多面体中具有最少的超面和尖点总数。这一事实被用于证明主要结果
We show that the right-angled hyperbolic polyhedra of finite volume in the hyperbolic space $\Bbb H^n$ may only exist if $n\leq 14.$ We also provide a family of such polyhedra of dimensions $n=3,4,...,8$. We prove that for $n=3,4$ the members of this family have the minimal total number of hyperfaces and cusps among all hyperbolic right-angled polyhedra of the corresponding dimension. This fact is used in the proof of the main result