A volume formula for generalized hyperbolic tetrahedra
| dc.creator | Ushijima, Akira | |
| dc.date | 2003-09-12 | |
| dc.date | 2003-10-30 | |
| dc.date.accessioned | 2026-07-07T05:01:05Z | |
| dc.date.available | 2026-07-07T05:01:05Z | |
| dc.description | A generalized hyperbolic tetrahedra is a polyhedron (possibly non-compact) 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 ones. There are two key tools for the proof; one is so-called Schlafli'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 generalized hyperbolic simplex with respect to their dihedral angles. | |
| dc.description | 18 pages, 4 figures, minor errors corrected and two references are added. To appear in "Non-Euclidean Geometries, Ja'nos Bolyai memorial volume ...", by Kluwer Academic Press | |
| dc.identifier | https://arxiv.org/abs/math/0309216 | |
| dc.identifier | http://arxiv.org/abs/math/0309216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68553 | |
| dc.subject | Geometric Topology | |
| dc.subject | Metric Geometry | |
| dc.subject | 52A38 (Primary) 51M09 (Secondary) | |
| dc.title | A volume formula for generalized hyperbolic tetrahedra | |
| dc.type | text |