Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

We consider a compact hyperbolic tetrahedron of a general type. It is a convex hull of four points called vertices in the hyperbolic space H3. It can be determined by the set of six edge lengths up to isometry. For further considerations, we use the notion of edge matrix of the tetrahedron formed by hyperbolic cosines of its edge lengths. We establish necessary and sufficient conditions for the existence of a tetrahedron in H3. Then we find relations between their dihedral angles and edge lengths in the form of a cosine rule. Finally, we obtain exact integral formula expressing the volume of a hyperbolic tetrahedron in terms of the edge lengths. The latter volume formula can be regarded as a new version of classical Sforza's formula for the volume of a tetrahedron but in terms of the edge matrix instead of the Gram matrix.

Язык оригиналаанглийский
Номер статьи2140007
ЖурналJournal of Knot Theory and its Ramifications
Том30
Номер выпуска10
DOI
СостояниеОпубликовано - 1 сен 2021

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