论文标题
音量保存右撇子矢量场是共同的REEB
Volume-preserving right-handed vector fields are conformally Reeb
论文作者
论文摘要
右撇子和Reeb矢量场是封闭的，定向的三个manifolds上的两个丰富的矢量字段。 DeHornoy和Florio-Hryniewicz的先前工作已经制作了许多Reeb矢量场的例子，这些例子是右手的。我们证明了另一个方向的结果。我们表明，与音量保护右手矢量场相关的封闭两种形式是接触类型。这意味着任何具有音量的右手矢量场都等于乘以正平滑函数后的Reeb矢量场。将我们的结果与GHYS和TAUBES定理相结合，表明任何具有量量的右撇子矢量场都有整体的全局表面。
Right-handed and Reeb vector fields are two rich classes of vector fields on closed, oriented three-manifolds. Prior work of Dehornoy and Florio-Hryniewicz has produced many examples of Reeb vector fields which are right-handed. We prove a result in the other direction. We show that the closed two-form associated to a volume-preserving right-handed vector field is contact-type. This implies that any volume-preserving right-handed vector field is equal to a Reeb vector field after multiplication by a positive smooth function. Combining our result with theorems of Ghys and Taubes shows that any volume-preserving right-handed vector field has a global surface of section.
