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| Главный автор: | |
|---|---|
| Формат: | Preprint |
| Опубликовано: |
2018
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| Предметы: | |
| Online-ссылка: | https://arxiv.org/abs/1804.08452 |
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Оглавление:
- In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler $n$-manifold with finite fundamental group and $n\ge 2$. Thus generically there are at least two closed geodesics on compact Finsler manifolds with finite fundamental group. Furthermore, there are at least two closed geodesics on any compact Finsler $2$-manifold, and this lower bound is achieved by the Katok 2-sphere $(S^2, F)$ and 2-real projective space $(S^2/\Z_2, F)$, cf. \cite{Kat}.