三维可嵌入CR结构的流动和相切条件
Flows and a tangency condition for embeddable CR structures in dimension 3
摘要：
我们研究了三维$CR$结构在几何流下的可填充性（或可嵌入性）。假设我们可以解出一个二阶方程，来得到与流动相关的几何量。然后我们证明，如果初始的$CR$结构是可填充的，那么它保持相同的属性，只要流有一个解决方案。我们讨论了扭转流和Cartan流的情况。在第二部分中，我们证明了上述二阶算子用于表示所有可填充或可嵌入的$CR$结构在$\mathbb{C}^{2}.$中嵌入一个的空间的相切条件
英文摘要：
We study the fillability (or embeddability) of 3-dimensional $CR$ structures under the geometric flows. Suppose we can solve a certain second order equation for the geometric quantity associated to the flow. Then we prove that if the initial $CR$ structure is fillable, then it keeps having the same property as long as the flow has a solution. We discuss the situation for the torsion flow and the Cartan flow. In the second part, we show that the above mentioned second order operator is used to express a tangency condition for the space of all fillable or embeddable $CR$ structures at one embedded in $\mathbb{C}^{2}.$
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