Alonso-Blanco, Ricardo J.; Blázquez-Sanz, David The only global contact transformations of order two or more are point transformations. (English) Zbl 1073.58006 J. Lie Theory 15, No. 1, 135-143 (2005). The authors consider the space of \(k\)-th jets of \(m\)-dimensional submanifolds \(J^k_mM\) of a smooth manifold \(M\). As is well-known, \(J^k_mM\) has a natural distribution which is spanned by the tangent planes to every prolonged \(m\)-dimensional submanifold of \(M\). A contact transformation of \(J^k_mM\) is a diffeomorphism of \(J^k_mM\) which preserves the Cartan distribution on \(J^k_mM\). Here it is proven that every contact transformation of \(J^k_mM\) is the prolongation of a diffeomorphism of \(M\) in the case \(k\geq 2\). Reviewer: Raffaele Vitolo (Lecce) Cited in 2 Documents MSC: 58A20 Jets in global analysis 58A30 Vector distributions (subbundles of the tangent bundles) Keywords:jets of submanifolds; contact transformations; point transformations. PDFBibTeX XMLCite \textit{R. J. Alonso-Blanco} and \textit{D. Blázquez-Sanz}, J. Lie Theory 15, No. 1, 135--143 (2005; Zbl 1073.58006) Full Text: EuDML