Affine curvature of plane geodesic lines on affine hypersurfaces
We establish a necessary and sufficient condition for a geodesic line on a nondegenerate hypersurface to be a plane curve. We deduce a formula for the affine curvature of a plane geodesic line on the affine hypersurface in terms of the affine fundamental form and the shape operator. We present the d...
Збережено в:
| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2017
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1716 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We establish a necessary and sufficient condition for a geodesic line on a nondegenerate hypersurface to be a plane curve.
We deduce a formula for the affine curvature of a plane geodesic line on the affine hypersurface in terms of the affine
fundamental form and the shape operator. We present the definition of transverse curvature and determine some of its
elementary properties. |
|---|