论文标题
接触叶和广义的温斯坦猜想
Contact foliations and generalised Weinstein conjectures
论文作者
论文摘要
我们考虑接触叶子：将较高维度推广到触点歧管上的Reeb矢量场的流动的对象。我们列出了此类叶子的许多特性，并提出了两种关于其叶子拓扑类型的猜想，在接触流的情况下，这两者都与经典的Weinstein猜想相吻合。在特定情况下，我们给我们的猜想给出了积极的部分结果 - 例如，当接触叶叶的全能保留了riemannian指标时 - 扩展了已经从接触动力学领域中建立的结果。
We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list a number of properties of such foliations, and propose two conjectures about the topological types of their leaves, both of which coincide with the classical Weinstein conjecture in the case of contact flows. We give positive partial results for our conjectures in particular cases -- when the holonomy of the contact foliation preserves a Riemannian metric, for instance -- extending already established results from the field of Contact Dynamics.
