A volume formula for hyperbolic tetrahedra in terms of edge lengths

被引：16

作者：

Murakami, Jun ^{[1
]}

Ushijima, Akira ^{[2
]}

机构：

[1] Waseda Univ, Sch Sci & Engn, Dept Math Sci, Tokyo 1698555, Japan

[2] Kanazawa Univ, Fac Sci, Dept Math, Kanazawa, Ishikawa 9201192, Japan

来源：

JOURNAL OF GEOMETRY | 2005年 / 83卷 / 1-2期

关键词：

Hyperbolic tetrahedron; quantum; 6j-symbol; volume formula;

D O I：

10.1007/s00022-005-0010-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a closed formula for volumes of generic hyperbolic tetrahedra in terms of edge lengths. The cue of our formula is by the volume conjecture for the Turaev-Viro invariant of closed 3-manifolds, which is defined from the quantum 6j-symbols. This formula contains the dilogarithm functions, and we specify the adequate branch to get the actual value of the volumes.

引用

页码：153 / 163

页数：11

共 50 条

[1] Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths
Abrosimov, Nikolay
Vuong, Bao
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2021, 30 (10)
[2] On the volume formula for hyperbolic tetrahedra
Cho, YH
Kim, H
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 1999, 22 (03) : 347 - 366
[3] On the Volume Formula for Hyperbolic Tetrahedra
[J]. Discrete & Computational Geometry, 1999, 22 : 347 - 366
[4] A volume formula for generalised hyperbolic tetrahedra
Ushijima, A
[J]. Non-Euclidean Geometries, 2006, 581 : 249 - 265
[5] ON INFINITESIMAL SYMMETRIZATION AND VOLUME FORMULA FOR SPHERICAL OR HYPERBOLIC TETRAHEDRA
HSIANG, WY
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1988, 39 (156): : 463 - 468
[6] A volume formula for asymptotic hyperbolic tetrahedra with an application to quantum field theory
Wagner, P
[J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 1996, 7 (04): : 527 - 547
[7] On volumes of truncated tetrahedra with constrained edge lengths
R. Frigerio
Marco Moraschini
[J]. Periodica Mathematica Hungarica, 2019, 79 : 32 - 49
[8] On volumes of truncated tetrahedra with constrained edge lengths
Frigerio, R.
Moraschini, Marco
[J]. PERIODICA MATHEMATICA HUNGARICA, 2019, 79 (01) : 32 - 49
[9] Reconstruction of tetrahedra from sets of edge lengths
N. O. Ermilov
[J]. Mathematical Notes, 2012, 91 : 500 - 507
[10] Reconstruction of tetrahedra from sets of edge lengths
Ermilov, N. O.
[J]. MATHEMATICAL NOTES, 2012, 91 (3-4) : 500 - 507

← 1 2 3 4 5 →