Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
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DOI：
10.2140/gt.2019.23.3601
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发表时间：
2017-01
影响因子：
2
通讯作者：
Daniel Cristofaro-Gardiner;M. Hutchings;Daniel Pomerleano
中科院分区：
文献类型：
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作者：
Daniel Cristofaro-Gardiner;M. Hutchings;Daniel Pomerleano
证明了连通三流形上的每个非退化接触形式，使得其相应的接触结构具有挠第一陈氏类，都有两个或无穷多个简单Reeb轨道.根据已有的结果，在上述假设下，如果三元流形不是三球面或透镜空间，则存在无穷多个简单Reeb轨道.我们还表明，对于非扭转接触结构，每个非退化接触形式至少有四个简单的Reeb轨道。
We prove that every nondegenerate contact form on a closed connected three-manifold, such that the associated contact structure has torsion first Chern class, has either two or infinitely many simple Reeb orbits. By previous results it follows that under the above assumptions, there are infinitely many simple Reeb orbits if the three-manifold is not the three-sphere or a lens space. We also show that for non-torsion contact structures, every nondegenerate contact form has at least four simple Reeb orbits.