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At first we introduce an action for the string, which leads to a worldsheetthat always is curved. For this action we study the Poincar\'e symmetry and theassociated 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 toWeyl invariant models.

Actions for the Bosonic String with the Curved Worldsheet