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Foliations of codimension one and the Milnor conjecture
Dmitry V. Bolotov B. Verkin Institute for Low Temperature Physics and Engineering of the National
Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
Аннотация:
We prove that a fundamental group of leaves of a codimension one $C^2$-foliation with nonnegative Ricci curvature on a closed Riemannian manifold is finitely generated and almost Abelian, i.e., it contains finitely generated Abelian subgroup of finite index. In particular, we confirm the Milnor conjecture for manifolds which are leaves of a codimension one foliation with nonnegative Ricci curvature on a closed Riemannian manifold.
Ключевые слова и фразы:
codimension one foliation, fundamental group, holonomy, Ricci curvature.
Поступила в редакцию: 30.05.2017 Исправленный вариант: 31.07.2017
Образец цитирования:
Dmitry V. Bolotov, “Foliations of codimension one and the Milnor conjecture”, Журн. матем. физ., анал., геом., 14:2 (2018), 119–131
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag692 https://www.mathnet.ru/rus/jmag/v14/i2/p119
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Страница аннотации: | 133 | PDF полного текста: | 42 | Список литературы: | 19 |
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