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The only global contact transformations of order two or more are point transformations. (English) Zbl 1073.58006

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 \(k\geq 2\).

MSC:

58A20 Jets in global analysis
58A30 Vector distributions (subbundles of the tangent bundles)
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