Abstract
A generalised hyperbolic tetrahedron is a polyhedron (possibly noncompact) with finite volume in hyperbolic space, obtained from a tetrahedron by the polar truncation at the vertices lying outside the space. In this paper it is proved that a volume formula for ordinary hyperbolic tetrahedra devised by J. Murakami and M. Yano can be applied to such generalised tetrahedra. There are two key tools for the proof; one is the so-called Schläfli’s differential formula for hyperbolic polyhedra, and the other is a necessary and sufficient condition for given numbers to be the dihedral angles of a generalised hyperbolic simplex with respect to their dihedral angles.
This research was partially supported by the Inamori Foundation.
Current e-mail address: ushijima@maths.warwick.ac.uk
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Ushijima, A. (2006). A Volume Formula for Generalised Hyperbolic Tetrahedra. In: Prékopa, A., Molnár, E. (eds) Non-Euclidean Geometries. Mathematics and Its Applications, vol 581. Springer, Boston, MA. https://doi.org/10.1007/0-387-29555-0_13
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DOI: https://doi.org/10.1007/0-387-29555-0_13
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