Foliations on closed three-dimensional Riemannian manifolds with small modulus of mean curvature of the leaves
- Авторлар: Bolotov D.V.1
-
Мекемелер:
- B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine
- Шығарылым: Том 86, № 4 (2022)
- Беттер: 85-102
- Бөлім: Articles
- URL: https://ogarev-online.ru/1607-0046/article/view/133874
- DOI: https://doi.org/10.4213/im9124
- ID: 133874
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
We prove that the modulus of mean curvature of the leaves of a transversely orientedfoliation of codimension one with a generalized Reeb component on an oriented smoothclosed three-dimensional Riemannian manifold cannot be everywhere smaller than a certainpositive constant depending on the volume, the maximum value of the sectional curvature,and the injectivity radius of the manifold. This means that foliations withsmall modulus of mean curvature of the leaves are taut.
Негізгі сөздер
Авторлар туралы
Dmitrii Bolotov
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of UkraineDoctor of physico-mathematical sciences, Senior Researcher
Әдебиет тізімі
- И. Тамура, Топология слоений, Мир, М., 1979, 319 с.
- D. Sullivan, “A homological characterization of foliations consisting of minimal surfaces”, Comment. Math. Helv., 54:2 (1979), 218–223
- A. Т. Фоменко, Д. Б. Фукс, Курс гомотопической топологии, Наука, М., 1989, 496 с.
- P. M. Pu, “Some inequalities in certain nonorientable Riemannian manifolds”, Pacific J. Math., 2 (1952), 55–71
- Ю. Д. Бураго, В. А. Залгаллер, Введение в риманову геометрию, Наука, СПб., 1994, 319 с.
- С. П. Новиков, “Топология слоений”, Тр. ММО, 14, Изд-во Моск. ун-та, М., 1965, 248–278
- A. Candel, L. Conlon, Foliations II, Grad. Stud. Math., 60, Amer. Math. Soc., Providence, RI, 2003, xiv+545 pp.
- Э. Спеньер, Алгебраическая топология, Мир, М., 1971, 680 с.
- Р. Ботт, Л. В. Ту, Дифференциальные формы в алгебраической топологии, Наука, М., 1989, 336 с.
Қосымша файлдар
