  A novel algorithm is provided to couple a Galilean invariant model with
curved spatial background by taking nonrelativistic limit of a unique minimally
coupled relativistic theory, which ensures Galilean symmetry in the flat limit
and canonical transformation of the original fields. That the twin requirements
are fulfilled is ensured by a new field, the existence of which was
demonstrated recently from Galilean gauge theory. The ambiguities and anomalies
concerning the recovery of Galilean symmetry in the flat limit of spatial non
relativistic diffeomorphic theories, reported in the literature, are focused
and resolved from a new angle.
