N. Abrosimov, S. Stepanishchev, “The volume of a trirectangular hyperbolic tetrahedron”, Sib. Èlektron. Mat. Izv., 2023, Volume 20, Issue 1,Pages <nobr>275

Geometry and topology

The volume of a trirectangular hyperbolic tetrahedron

N. Abrosimov^ab, S. Stepanishchev^c

^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

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.

UDC: 514.132

MSC: 51M20, 51M25, 51M10

Received December 17, 2022, published March 13, 2023

Language: English

DOI: 10.33048/semi.2023.20.022