Special Warped-Like Product Manifolds with (Weak) G₂ Holonomy
By using fiber-base decomposition of the manifolds, the definition of warped-like product is considered as a generalization of multiply-warped product manifolds, by allowing the fiber metric to be not block diagonal. We consider (3 + 3 + 1) decomposition of 7-dimensional warped-like product manifo...
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| Дата: | 2013 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/165602 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Special Warped-Like Product Manifolds with (Weak) G₂ Holonomy / S. Uğuz // Український математичний журнал. — 2013. — Т. 65, № 8. — С. 1126–1140. — Бібліогр.: 36 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | By using fiber-base decomposition of the manifolds, the definition of warped-like product is considered as a generalization
of multiply-warped product manifolds, by allowing the fiber metric to be not block diagonal. We consider (3 + 3 + 1)
decomposition of 7-dimensional warped-like product manifolds, which is called a special warped-like product of the form
M = F × B, where the base B is a one-dimensional Riemannian manifold and the fibre F is of the form F = F₁ × F₂
where Fi, i = 1, 2, are Riemannian 3-manifolds. If all fibers are complete, connected, and simply connected, then the
fibers are isometric to S³ with constant curvature k > 0 in the class of special warped-like product metrics admitting the
(weak) G₂ holonomy determined by the fundamental 3-form. |
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