A characterization of totally umbilical hypersurfaces of a space form by geodesic mapping
The idea of considering the second fundamental form of a hypersurface as the first fundamental form of another hypersurface has found very useful applications in Riemannian and semi-Riemannian geometry, specially when trying to characterize extrinsic hyperspheres and ovaloids. Recently, T. Adachi...
Збережено в:
| Дата: | 2013 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2013
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2441 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | The idea of considering the second fundamental form of a hypersurface as the first fundamental form of another hypersurface has found very useful applications in
Riemannian and semi-Riemannian geometry, specially when trying to characterize extrinsic hyperspheres and ovaloids.
Recently, T. Adachi and S. Maeda gave a characterization of totally umbilical hypersurfaces in a space form by circles.
In this paper, we give a characterization of totally umbilical hypersurfaces of a space form by means of geodesic mapping. |
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