Hyperplanar Webs and Euler Equations
We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, . . . , xn) to be totally geodesic in a torsion-free connection and apply them to find the conditions for d-webs of hypersurfaces to be geodesic, and in the case of flat connections, for d-webs (d...
Збережено в:
| Дата: | 2009 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/6308 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hyperplanar Webs and Euler Equations / V.V. Goldberg, V.V. Lychagin // Збірник праць Інституту математики НАН України. — 2009. — Т. 6, № 2. — С. 276-287. — Бібліогр.: 1 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, . . . , xn) to be totally geodesic in a torsion-free connection and apply them to find the conditions for d-webs of hypersurfaces to be geodesic, and in the case of flat connections, for d-webs (d ≥ n + 1) of hypersurfaces to be hyperplanar webs. These conditions are systems of generalized Euler equations, and for flat connections we give an explicit construction of their solutions. |
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