Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths Научная публикация
| Журнал |
Journal of Knot Theory and its Ramifications
ISSN: 0218-2165 |
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| Вых. Данные | Год: 2021, Том: 30, Номер: 10, Номер статьи : 2140007, Страниц : 13 DOI: 10.1142/s0218216521400071 | ||||||
| Ключевые слова | edge matrix; Hyperbolic tetrahedron; hyperbolic volume; Sforza's formula | ||||||
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Реферат:
We consider a compact hyperbolic tetrahedron of a general type. It is a convex hull of four points called vertices in the hyperbolic space H^3. 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 H^3. 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.
Библиографическая ссылка:
Abrosimov N.
, Vuong B.
Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths
Journal of Knot Theory and its Ramifications. 2021. V.30. N10. 2140007 :1-13. DOI: 10.1142/s0218216521400071 WOS Scopus OpenAlex
Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths
Journal of Knot Theory and its Ramifications. 2021. V.30. N10. 2140007 :1-13. DOI: 10.1142/s0218216521400071 WOS Scopus OpenAlex
Даты:
| Опубликована online: | 9 дек. 2021 г. |
Идентификаторы БД:
| Web of science: | WOS:000743509300007 |
| Scopus: | 2-s2.0-85121263044 |
| OpenAlex: | W3181136734 |