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0410U001210,
к.ф.-м.н.
11-01-2010
o
Parabolic and saddle foliations and distributions on 3-manifolds.
Kruglov Volodymyr Volodymyrovich,
popup.head Borisenko Alexander Andreevich
popup.opponent Зарічний Михайло Михайлович
popup.opponent Пришляк Олександр Олегович
В дисертації вивчаються контактні структури та шарування на замкнених тривимірних многовидах. Мета дослідження полягає в вивченні зв'язку між геометричними та топологічними властивостями шарувань і контактних структур. Основними методами дослідження є ріманова геометрія, геометрична топологія, метод Бохнера. В дисертації доведено такі основні результати: доведена теорема уніформізації контактних структур на замкнених тривимірних многовидах, доведено, що на кожному замкненому тривимірному многовиді існують параболічні та сідлові шарування, доведено, що всі контактні структури із равним нулю класом Ейлера є сідловими, доведено, що всі контактні структури на замкнених тривимірних многовидах є параболічними, вирішено питання існівання цілком геодезичних контактних структур на замкнених многовидах за зразком тьорстонівських геометрій.
2010-01-11
2020-04-04
Updated: 2025-12-08
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