The tubular neighborhood theorem in contact geometry

Consider a smooth manifold C and let H be a smooth distribution of hyperplanes on C, i.e., a subbundle of the tangent bundle T C of corank 1, H c_ TC. Such a distribution induces for any c ~ C a skew-symmetric bilinear form Wc : Hc • Hc -+ TCc/Hc given by the following. If~, ~ ~ Hc and X, Y E F ( H ) are arbitrary global sections in H extending ~ and ~, Xc = ~, Yc = ~, then it is easy to see that the ordinary Lie bracket [X, Y]c does not depend on the extensions if one looks at its coset class modulo He,