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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
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.
Received: 05.12.2017 Revised: 22.03.2019
Citation:
V. A. Krasnov, “On the Volumes of Hyperbolic Simplices”, Mat. Zametki, 106:6 (2019), 866–880; Math. Notes, 106:6 (2019), 909–921
Linking options:
https://www.mathnet.ru/eng/mzm11876https://doi.org/10.4213/mzm11876 https://www.mathnet.ru/eng/mzm/v106/i6/p866
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Abstract page: | 264 | Full-text PDF : | 59 | References: | 33 | First page: | 11 |
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