A volume formula for hyperbolic tetrahedra in terms of edge lengths
Metric Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0402087,
title = {A volume formula for hyperbolic tetrahedra in terms of edge lengths},
author = {Jun Murakami and Akira Ushijima},
journal= {arXiv preprint arXiv:math/0402087},
year = {2007}
}
Comments
12 pages, 1 figure