Geodesic
The Only Global Contact Transformations of Order Two or More are Point Transformations
Journal of Lie Theory, Tome 15 (2005) no. 1, pp. 135-143

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We consider the space JmkM of k-jets of m-dimensional submanifolds of a smooth manifold M. Our purpose is to show that every contact transformation of JmkM, k ≥ 2, is induced by a diffeomorphism of M (point transformations). It is also derived that a first order contact transformation can not be globally prolonged to higher order jets except when it is a point transformation. This holds true as well for jets of sections of a regular projection. The Legendre transformation gives us an example of this property.
Classification : 58A20, 58A30
Mots-clés : Jet, contact system, contact transformation 
R. J. Alonso-Blanco; D. Blázquez-Sanz. The Only Global Contact Transformations of Order Two or More are Point Transformations. Journal of Lie Theory, Tome 15 (2005) no. 1, pp. 135-143. http://geodesic.mathdoc.fr/item/JOLT_2005_15_1_a9/
@article{JOLT_2005_15_1_a9,
     author = {R. J. Alonso-Blanco and D. Bl\'azquez-Sanz},
     title = {The {Only} {Global} {Contact} {Transformations} of {Order} {Two} or {More} are {Point} {Transformations}},
     journal = {Journal of Lie Theory},
     pages = {135--143},
     year = {2005},
     volume = {15},
     number = {1},
     zbl = {1073.58006},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2005_15_1_a9/}
}
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