A volume formula for hyperbolic tetrahedra in terms of edge lengths

2004/02/05 by Jun Murakami, Murakami, Jun, Akira Ushijima +1 · 2 citations
Mathematics · #51M09 (Secondary) #52A38 (Primary) #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:51M09 #msc:52A38

paper · pdf · doi:10.48550/arxiv.math/0402087

12 pages, 1 figure

arxiv created 2004/02/05 · arxiv updated 2009/12/01

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.

Cited by

• On the Virasoro Crossing Kernels at Rational Central Charge
• Volumes of Regular Hyperbolic Simplices

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• Growth of quantum 6j-symbols and applications to the Volume Conjecture