A volume formula for hyperbolic tetrahedra in terms of edge lengths

Details A volume formula for hyperbolic tetrahedra in terms of edge lengths A volume formula for hyperbolic tetrahedra in terms of edge lengths

2004-02-05

arxiv.org/abs/math/0402087v1

Mathematics

Metric Geometry

12 pages, 1 figure

Scientific paper

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.

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