In these notes we associate a natural Heisenberg group bundle Ha with a singularity free smooth vector field
X = (id,a) on a submanifold M in a Euclidean three‐space. This bundle yields naturally an infinite dimensional Heisenberg group
. A representation of the C*‐group algebra of
is a quantization. It causes a natural Weyl‐deformation quantization of X. The influence of the topological structure of M on this quantization is encoded in the Chern class of a canonical complex line bundle inside Ha.