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 |
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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 |
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Keywords
- Hyperbolic tetrahedron
- Quantum 6j-symbol
- Volume formula
ASJC Scopus subject areas
- Geometry and Topology
Cite this
A volume formula for hyperbolic tetrahedra in terms of edge lengths. / Murakami, Jun; Ushijima, Akira.
In: Journal of Geometry, Vol. 83, No. 1-2, 12.2005, p. 153-163.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A volume formula for hyperbolic tetrahedra in terms of edge lengths
AU - Murakami, Jun
AU - Ushijima, Akira
PY - 2005/12
Y1 - 2005/12
N2 - 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.
AB - 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.
KW - Hyperbolic tetrahedron
KW - Quantum 6j-symbol
KW - Volume formula
UR - http://www.scopus.com/inward/record.url?scp=29744448338&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=29744448338&partnerID=8YFLogxK
U2 - 10.1007/s00022-005-0010-4
DO - 10.1007/s00022-005-0010-4
M3 - Article
AN - SCOPUS:29744448338
VL - 83
SP - 153
EP - 163
JO - Journal of Geometry
JF - Journal of Geometry
SN - 0047-2468
IS - 1-2
ER -