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June 2016 The Dual Jacobian of a Generalised Hyperbolic Tetrahedron, and Volumes of Prisms
Alexander KOLPAKOV, Jun MURAKAMI
Tokyo J. Math. 39(1): 45-67 (June 2016). DOI: 10.3836/tjm/1471873312

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.

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Alexander KOLPAKOV. Jun MURAKAMI. "The Dual Jacobian of a Generalised Hyperbolic Tetrahedron, and Volumes of Prisms." Tokyo J. Math. 39 (1) 45 - 67, June 2016. https://doi.org/10.3836/tjm/1471873312

Information

Published: June 2016
First available in Project Euclid: 22 August 2016

zbMATH: 1358.51014
MathSciNet: MR3543131
Digital Object Identifier: 10.3836/tjm/1471873312

Rights: Copyright © 2016 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 1 • June 2016
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