Універсальні багатоточкові інваріанти та геометрія просторів сталої кривини
The geometric properties of a two-dimensional constant curvature space are presented as a consequence of existence in it of a universal multipoint invariant (к)Δ24, which has the form of a determinant of the corresponding matrix. The metrics and analytical equations of geodesics in a bipolar system...
Збережено в:
| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Ukrainian |
| Опубліковано: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2018
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| Теми: | |
| Онлайн доступ: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/2285 |
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| Назва журналу: | Prykladni Problemy Mekhaniky i Matematyky |
Репозитарії
Prykladni Problemy Mekhaniky i Matematyky| Резюме: | The geometric properties of a two-dimensional constant curvature space are presented as a consequence of existence in it of a universal multipoint invariant (к)Δ24, which has the form of a determinant of the corresponding matrix. The metrics and analytical equations of geodesics in a bipolar system of radial coordinates are found by this invariant. It is shown that the basic metrical relations, and also the constant Gaussian curvature, which are characteristic for the two-dimensional sphere and the Lobachevsky plane, can be obtained as a result of the invariant (к)Δ24 analysis. Cite as: Dziakovych D. A. Universal multipoint invariants and geometry of constant curvature spaces // Appl. Probl. Mech. Math. – 2017. – No. 15. – С. 42–49. [In Ukrainian] |
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