Two closed geodesics on compact simply connected bumpy Finsler manifolds
Two closed geodesics on compact simply connected bumpy Finsler manifolds
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DOI：
10.4310/jdg/1476367058
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发表时间：
2016-10
影响因子：
2.5
通讯作者：
Huagui Duan;Y. Long;Wei Wang
中科院分区：
文献类型：
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作者：
Huagui Duan;Y. Long;Wei Wang
我们证明了在具有凹凸不平且不可逆的芬斯勒度量的紧致单连通流形 M 上存在至少两个不同的闭合测地线，当 H ∗ ( M ; Q ) ∼ = T d,h +1 ( x ) 对于某个整数 h ≥ 2 甚至整数 d ≥ 2 时。因此，与 S n 的早期结果一起，这意味着在每个紧连通流形上至少存在两个不同的闭合测地线 M 具有坎坷不可逆芬斯勒度量。
We prove the existence of at least two distinct closed geodesics on a compact simply connected manifold M with a bumpy and irreversible Finsler metric, when H ∗ ( M ; Q ) ∼ = T d,h +1 ( x ) for some integer h ≥ 2 and even integer d ≥ 2. Consequently, together with earlier results on S n , it implies the existence of at least two distinct closed geodesics on every compact simply connected manifold M with a bumpy irreversible Finsler metric.