Abstract
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.
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After this paper was submitted, [15] was posted to the arXiv which deals with the C1 case for all rigid groups. The author, Jona Lelmi, uses a striking new characterization of weakly contact vector fields.
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Acknowledgements
The author thanks Alessandro Ottazzi for comments on the Tanaka prolongation of a stratified Lie algebra, Francesco Serra Cassano for elaborating on the proof of Lemma 3.3 and Ben Warhurst for suggesting the Cartan group as suitable test case.
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Austin, A.D. The contact mappings of a flat (2,3,5)-distribution. Ann Glob Anal Geom 60, 143–156 (2021). https://doi.org/10.1007/s10455-021-09767-4
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DOI: https://doi.org/10.1007/s10455-021-09767-4