The contact mappings of a flat $(2,3,5)$-distribution

Abstract

Let $\Omega$ and ${\Omega }^{\prime }$ be open subsets of a flat $(2,3,5)$-distribution. We show that a $C^1$-smooth contact mapping $f:\Omega \to {\Omega }^{\prime }$ 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 $C^1$-smooth contact mapping.

arXiv comment16 pages