The dual jacobian of a generalised hyperbolic tetrahedron, and volumes of prisms

Alexander Kolpakov, Jun Murakami

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the corresponding volume formulae. Also, we obtain a volume formula for a hyperbolic n-gonal prism: the proof requires the above mentioned Jacobian, employed in the analysis of the edge lengths behaviour of such a prism, needed later for the Schläfli formula.

    Original languageEnglish
    Pages (from-to)45-67
    Number of pages23
    JournalTokyo Journal of Mathematics
    Volume39
    Issue number1
    Publication statusPublished - 2016 Jun 1

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    Prism
    Triangular pyramid
    Volume formula
    Truncated tetrahedron
    Analytic Continuation
    Jacobian matrix
    Line

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    The dual jacobian of a generalised hyperbolic tetrahedron, and volumes of prisms. / Kolpakov, Alexander; Murakami, Jun.

    In: Tokyo Journal of Mathematics, Vol. 39, No. 1, 01.06.2016, p. 45-67.

    Research output: Contribution to journalArticle

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