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
收藏
页码：153 / 163
页数：11
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