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Matematicheskie Zametki, 2019, Volume 106, Issue 6, Pages 866–880
DOI: https://doi.org/10.4213/mzm11876 (Mi mzm11876) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Volumes of Hyperbolic Simplices

V. A. Krasnov

Peoples' Friendship University of Russia, Moscow
Full-text PDF (615 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11876
Abstract: We present an explicit formula for calculating the volume of an arbitrary hyperbolic 4-simplex in terms of the coordinates of its vertices; by this formula, the volume can be expressed in terms of one-dimensional integrals of real-valued integrands over closed intervals of the real line. In addition, it is proved in the paper that the volume of a hyperbolic 5-simplex cannot be expressed as the double integral of an elementary function of the coordinates of its vertices (of edge lengths).
Keywords: volume, simplex, hyperbolic space.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
This work was supported by the RUDN program “5-100.”
Received: 05.12.2017
Revised: 22.03.2019
English version:
Mathematical Notes, 2019, Volume 106, Issue 6, Pages 909–921
DOI: https://doi.org/10.1134/S0001434619110270
Bibliographic databases:
Document Type: Article
UDC: 514.13+514.132
Language: Russian
Citation: V. A. Krasnov, “On the Volumes of Hyperbolic Simplices”, Mat. Zametki, 106:6 (2019), 866–880; Math. Notes, 106:6 (2019), 909–921
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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