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.
| Original language | English |
|---|---|
| Pages (from-to) | 153-163 |
| Number of pages | 11 |
| Journal | Journal of Geometry |
| Volume | 83 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 2005 Dec 1 |
Keywords
- Hyperbolic tetrahedron
- Quantum 6j-symbol
- Volume formula
ASJC Scopus subject areas
- Geometry and Topology
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Cite this
Murakami, J., & Ushijima, A. (2005). A volume formula for hyperbolic tetrahedra in terms of edge lengths. Journal of Geometry, 83(1-2), 153-163. https://doi.org/10.1007/s00022-005-0010-4