We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show ${\mathbb{S}}^3$ does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a contact structure implying that a Reeb field is Anosov. From this we can give curvature conditions on a metric compatible with a contact structure that implies universal tightness of the contact structure among other things.

中文翻译：

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保形Anosov接触3流形的动力学和拓扑

我们为三流形上共形Anosov Reeb流的存在提供了障碍，该流形部分地泛化了与Anosov Reeb流相似的障碍。特别是，我们展示${\mathbb{小号}}^3$不允许共形的Anosov Reeb流动。我们还给出了与接触结构兼容的度量的黎曼几何条件，这表明里布场是阿诺索夫。据此，我们可以给出与接触结构兼容的度量标准上的曲率条件，这暗示了接触结构的普遍紧密性。