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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 1, Pages 275–284
DOI: https://doi.org/10.33048/semi.2023.20.022 (Mi semr1586) 		 
Geometry and topology

The volume of a trirectangular hyperbolic tetrahedron

N. Abrosimovab, S. Stepanishchevc

a Regional Scientific and Educational Mathematical Center, Tomsk State University, pr. Lenina, 36, 634050, Tomsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
c Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2023.20.022
Abstract: We consider a three-parameter family of tetrahedra in the hyperbolic space, which three edges at one vertex are pairwise orthogonal. It is convenient to determine such tetrahedra by the lengths of these edges. We obtain relatively simple formulas for them expressing the volume and the surface area. This allows us to find normalized volume and investigate its asymptotics.
Keywords: hyperbolic volume, normalized volume, Poincaré upper half-space model, hyperbolic tetrahedron, trirectangular tetrahedron, infinite cone.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2023-943
This work was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2023-943).
Received December 17, 2022, published March 13, 2023
Document Type: Article
UDC: 514.132
MSC: 51M20, 51M25, 51M10
Language: English
Citation: N. Abrosimov, S. Stepanishchev, “The volume of a trirectangular hyperbolic tetrahedron”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 275–284
Citation in format AMSBIB
\Bibitem{AbrSte23}
\by N.~Abrosimov, S.~Stepanishchev
\paper The volume of a trirectangular hyperbolic tetrahedron
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 1
\pages 275--284
\mathnet{http://mi.mathnet.ru/semr1586}
\crossref{https://doi.org/10.33048/semi.2023.20.022}
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