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Applying the loop variable proposal to a sigma model (with boundary) in acurved target space, we give a systematic method for writing the gauge andgenerally covariant interacting equations of motion for the modes of the openstring in a curved background. As in the free case described in an earlierpaper, the equations are obtained by covariantizing the flat space (gaugeinvariant) interacting equations and then demanding gauge invariance in thecurved background. The resulting equation has the form of a sum of terms thatwould individually be gauge invariant in flat space or at zero interactionstrength, but mix amongst themselves in curved space when interactions areturned on. The new feature is that the loop variables are deformed so thatthere is a mixing of modes. Unlike the free case, the equations are coupled,and all the modes of the open string are required for gauge invariance.Comment: 11 pages, Late

LOOP VARIABLES AND THE INTERACTING OPEN STRING IN A CURVED BACKGROUND