Journal of Lie Theory 15 (2005), No. 1, 135--143
Copyright Heldermann Verlag 2005
The Only Global Contact Transformations of Order Two or More are Point Transformations
Ricardo J. Alonso-Blanco
Dep. de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain
ricardo@usal.es
David Blázquez-Sanz
Dep. de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain
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.
Keywords: Jet, contact system, contact transformation.
MSC: 58A20; 58A30
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