Closed geodesics on connected sums and 3-manifolds Научная публикация
| Журнал |
Journal of Differential Geometry
ISSN: 0022-040X , E-ISSN: 1945-743X |
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| Вых. Данные | Год: 2022, Том: 120, Номер: 3, Страницы: 557-573 Страниц : 17 DOI: 10.4310/jdg/1649953350 | ||||||
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Реферат:
We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of length
≤ t of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at least three with non-trivial fundamental groups, and apply the results to the prime decomposition of a three-manifold. In particular we show that the function N(t) grows at least like the prime numbers on a compact 3-manifold with infinite fundamental group. It follows that a generic Riemannian metric on a compact 3-manifold has infinitely many geometrically distinct closed geodesics. We also consider the case of a connected sum of a compact manifold with positive first Betti number and a simplyconnected manifold which is not homeomorphic to a sphere.
Библиографическая ссылка:
Rademacher H.-B.
, Taimanov I.A.
Closed geodesics on connected sums and 3-manifolds
Journal of Differential Geometry. 2022. V.120. N3. P.557-573. DOI: 10.4310/jdg/1649953350 WOS Scopus РИНЦ OpenAlex
Closed geodesics on connected sums and 3-manifolds
Journal of Differential Geometry. 2022. V.120. N3. P.557-573. DOI: 10.4310/jdg/1649953350 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 12 сент. 2018 г. |
| Принята к публикации: | 7 янв. 2020 г. |
| Опубликована online: | 15 апр. 2022 г. |
Идентификаторы БД:
| Web of science: | WOS:000789251200006 |
| Scopus: | 2-s2.0-85130106876 |
| РИНЦ: | 48584841 |
| OpenAlex: | W2892237837 |