Geodesic
On the Volumes of Hyperbolic Simplices
Matematičeskie zametki, Tome 106 (2019) no. 6, pp. 866-880

Voir la notice de l'article provenant de la source Math-Net.Ru

We present an explicit formula for calculating the volume of an arbitrary hyperbolic 4-simplex in terms of the coordinates of its vertices; by this formula, the volume can be expressed in terms of one-dimensional integrals of real-valued integrands over closed intervals of the real line. In addition, it is proved in the paper that the volume of a hyperbolic 5-simplex cannot be expressed as the double integral of an elementary function of the coordinates of its vertices (of edge lengths).
Mots-clés : volume, simplex
Keywords: hyperbolic space. 
@article{MZM_2019_106_6_a7,
     author = {V. A. Krasnov},
     title = {On the {Volumes} of {Hyperbolic} {Simplices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {866--880},
     publisher = {mathdoc},
     volume = {106},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a7/}
}
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V. A. Krasnov. On the Volumes of Hyperbolic Simplices. Matematičeskie zametki, Tome 106 (2019) no. 6, pp. 866-880. http://geodesic.mathdoc.fr/item/MZM_2019_106_6_a7/