On right-angled reflection groups in hyperbolic spaces | Zendy

Leonid Potyagailo | Zendy; É. B. Vinberg | Zendy

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On right-angled reflection groups in hyperbolic spaces

Author(s) -

Leonid Potyagailo,

É. B. Vinberg

Publication year - 2005

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/4

Subject(s) - mathematics , reflection (computer programming) , pure mathematics , hyperbolic space , mathematical analysis , computer science , programming language

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

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