English

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