Existence of periodic orbits for geodesible vector fields on closed 3-manifolds
Existence of periodic orbits for geodesible vector fields on closed 3-manifolds
复制标题
闭三流形上测地向量场周期轨道的存在性
DOI：
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发表时间：
2009
影响因子：
0.9
通讯作者：
Ana Rechtman
中科院分区：
文献类型：
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作者：
Ana Rechtman
本文讨论了闭3流形上可测地向量场的周期轨道的存在性。如果在环境流形上存在一个黎曼度量使其轨道为测地线，则矢量场是可测地线的。特别是，Reeb矢量场和允许全局截面的矢量场是可测地线的。我们将分类承认非周期保体积Cω可测地向量场的闭3-流形，并证明当3-流形不是圆上的环面束时，Cω可测地向量场（非保体积）的周期轨道的存在性。我们还证明了在一些闭3流形上C2可测地向量场的周期轨道的存在性。
Abstract In this paper we deal with the existence of periodic orbits of geodesible vector fields on closed 3-manifolds. A vector field is geodesible if there exists a Riemannian metric on the ambient manifold making its orbits geodesics. In particular, Reeb vector fields and vector fields that admit a global section are geodesible. We will classify the closed 3-manifolds that admit aperiodic volume-preserving Cω geodesible vector fields, and prove the existence of periodic orbits for Cω geodesible vector fields (not volume preserving), when the 3-manifold is not a torus bundle over the circle. We will also prove the existence of periodic orbits of C2 geodesible vector fields on some closed 3-manifolds.