We consider evolution equations for curves in the 3-dimensional sphere $S^3$ that are invariant under the group $SU(2,1)$ of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we investigate how invariant evolutions of Legendrian and transverse curves induce both new and well-known integrable systems and hierarchies at the level of their geometric invariants.

中文翻译：

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伪保形S ^3中曲线的可积几何流

我们考虑3维球体中曲线的演化方程 ${\mathrm{小号}}^3$ 在组下是不变的 $\mathrm{小号}ü（\mathrm{2个}，\mathrm{1个}）$伪保形变换，它保留了球体上的标准接触结构。尤其是，我们研究了勒让德曲线和横向曲线的不变演化如何在其几何不变性的水平上引发新的和众所周知的可积系统和层次结构。