  The nonrelativistic bosonic string theory in a curved manifold is formulated
here using gauging of symmetry approach ( Galilean Gauge theory ) . The
corresponding model in flat space has some global symmetries . By localizing
these symmetries as per Galilean Gauge theory , the action for the
nonrelativistic string interacting with gravity is obtained. A canonical
analysis of the model has been performed which demonstrate that the
transformations of the basic field variables under gauge transformations in
phase space are equivalent to the diffeomorphism parameters by an exact
mapping. Thus complete consistency of our results from both Lagrangian and
Hamiltonian procedures are established.
