A volume formula for hyperbolic tetrahedra in terms of edge lengths

Jun Murakami; Akira Ushijima

doi:10.1007/s00022-005-0010-4

A volume formula for hyperbolic tetrahedra in terms of edge lengths

Jun Murakami, Akira Ushijima

Research output: Contribution to journal › Article

17 Citations (Scopus)

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	https://doi.org/10.1007/s00022-005-0010-4
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

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

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Access to Document

10.1007/s00022-005-0010-4