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

Abstract

Let Ω and Ω ′ be open subsets of a flat (2, 3, 5)-distribution. We show that a C 1 -smooth contact mapping f :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.

On the smoothness of $C^1$-contact maps in $C^{\infty}$-rigid Carnot groups

“…Nevertheless, we find that our definition captures better the properties of such vector fields and the coordinate free definition allows us to conclude smoothness of those fields in a transparent way. To conclude the proof of Theorem 1.1 in the special case of the (2,3,5) distributions the author of [1] clearly uses the special algebraic structure of them, while here we prove the statement for general C ∞ -rigid Carnot groups using mainly the properties of the dual action of contact fields on differential forms.…”

“…Extensions and limits of the strategy will be addressed in the Master thesis of the author [5]. After this work was completed the author learned that in a very recent work A. Austin [1] has proved Theorem 1.1 for the special case of (2, 3, 5) distributions. His proof already contains the idea of defining a certain notion of generalized contact fields that are shown to be smooth in every C ∞ -rigid Carnot group.…”