A volume formula for hyperbolic tetrahedra in terms of edge lengths

Jun Murakami, Akira Ushijima

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)153-163
Number of pages11
JournalJournal of Geometry
Volume83
Issue number1-2
DOIs
Publication statusPublished - 2005 Dec 1

Keywords

  • Hyperbolic tetrahedron
  • Quantum 6j-symbol
  • Volume formula

ASJC Scopus subject areas

  • Geometry and Topology

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