Necessary condition for the existence of a simple closed geodesic on a regular tetrahedron in the spherical space

• Published in: Доповіді НАН України
• Date: 2020
• Main Author: Sukhorebska, D.D.
• Format: Article
• Language: English
• Published: Видавничий дім "Академперіодика" НАН України 2020
• Subjects: Математика
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/173758
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...