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

    Fingerprint

    Volume formula
    Triangular pyramid
    Dilogarithm
    Closed
    Branch
    Invariant

    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

    Murakami, J & Ushijima, A 2005, 'A volume formula for hyperbolic tetrahedra in terms of edge lengths', Journal of Geometry, vol. 83, no. 1-2, pp. 153-163. https://doi.org/10.1007/s00022-005-0010-4
    Murakami J, Ushijima A. A volume formula for hyperbolic tetrahedra in terms of edge lengths. Journal of Geometry. 2005 Dec;83(1-2):153-163. https://doi.org/10.1007/s00022-005-0010-4
    Murakami, Jun ; Ushijima, Akira. / A volume formula for hyperbolic tetrahedra in terms of edge lengths. In: Journal of Geometry. 2005 ; Vol. 83, No. 1-2. pp. 153-163.
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