Let Ω and Ω′ be open subsets of a flat (2,3,5)-distribution. We show that a C¹-smooth contact mapping f: Ω → Ω′ is a \(C^\infty\)-smooth contact mapping. Ultimately, this is a consequence of the rigidity of the associated stratified Lie group. (The Tanaka prolongation of the Lie algebra is of finite type.) The conclusion is reached through a careful study of some differential identities satisfied by components of the Pansu derivative of a C¹-smooth contact mapping.

中文翻译：

---

平面（2,3,5）分布的接触映射

令Ω和Ω'是平坦（2,3,5）分布的开放子集。我们表明，C ^1-平滑接触映射f：Ω→Ω'是\（C ^ \ infty \）-平滑接触映射。最终，这是相关的分层Lie组僵化的结果。（Lie代数的Tanaka延拓是有限类型的。）通过仔细研究C ¹光滑接触映射的Pansu导数的成分满足的一些微分恒等式，可以得出结论。