Necessary condition for the existence of a simple closed geodesic on a regular tetrahedron in the spherical space
In the spherical space the curvature of the tetrahedron’s faces equals 1, and the curvature of the whole tetrahedron is concentrated into its vertices and faces. The intrinsic geometry of this tetrahedron depends on the value α of faces angle, where π/3 < α ≤ 2π/3. The simple (without points of...
Збережено в:
| Дата: | 2020 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Видавничий дім "Академперіодика" НАН України
2020
|
| Назва видання: | Доповіді НАН України |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/173758 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Necessary condition for the existence of a simple closed geodesic on a regular tetrahedron in the spherical space / D.D. Sukhorebska // Доповіді Національної академії наук України. — 2020. — № 10. — С. 9-14. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | In the spherical space the curvature of the tetrahedron’s faces equals 1, and the curvature of the whole tetrahedron
is concentrated into its vertices and faces. The intrinsic geometry of this tetrahedron depends on the value α
of faces angle, where π/3 < α ≤ 2π/3. The simple (without points of self-intersection) closed geodesic has the type
(p,q) on a tetrahedron, if this geodesic has p points on each of two opposite edges of the tetrahedron, q points on
each of another two opposite edges, and (p+q) points on each edges of the third pair of opposite one. For any coprime
integers (p,q), we present the number αp, q (π/3 < αp, q < 2π/3) such that, on a regular tetrahedron in the
spherical space with the faces angle of value α > αp, q, there is no simple closed geodesic of type (p,q). |
|---|