Actions for the bosonic string with the curved worldsheet

at first we introduce an action for the string, which leads to a worldsheet that always is curved. for this action we study the poincaré symmetry and the associated conserved currents. then, a generalization of the above action, which contains an arbitrary function of the two-dimensional scalar curvature, will be introduced. an extra scalar field enables us to modify these actions to weyl invariant models.