Abstract
We study the llability (or embeddability) of 3-dimensional CR structures under the geometric ows. Suppose we can solve a certain second order equation for the geometric quantity associated to the ow. Then we prove that if the initial CR structure is llable, then it keeps having the same property as long as the ow has a solution. We discuss the situation for the torsion ow and the Cartan ow. In the second part, we show that the above mentioned second order operator is used to express the tangency condition for the space of all llable or embeddable CR structures at one embedded in C 2 :
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