A volume formula for hyperbolic tetrahedra in terms of edge lengths
A volume formula for hyperbolic tetrahedra in terms of edge lengths
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DOI：
10.1007/s00022-005-0010-4
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发表时间：
2004-02
影响因子：
0.6
通讯作者：
J. Murakami;Akira Ushijima
中科院分区：
文献类型：
--
作者：
J. Murakami;Akira Ushijima
我们给出了一般双曲四面体体积的边长封闭公式。我们公式的线索是闭 3 流形的 Turaev-Viro 不变量的体积猜想，它是根据量子 6j 符号定义的。该公式包含二对数函数，我们指定适当的分支来获取体积的实际值。
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.