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Sep 10, 2013 at 17:16 comment added Oldřich Spáčil Yes, you can make the contactomorphism between a tubular nbhd of $K$ and the zero section of $J^{1}K$ preserve the contact forms, i.e. the jet contact form and your preferred contact form on your contact manifold. See Kriegl, Michor: The convenient setting of global analysis, Proposition 43.18.
Sep 10, 2013 at 6:55 history answered Giovanni Moreno CC BY-SA 3.0