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We classify the differential invariants and moving frames for surfaces in projective space under the action of the projective group. The role of these results in the analysis of Adler-Gel'fand-Dikii flows that arise in inverse scattering and solitons is explained.doi:10.4310/cag.1999.v7.n4.a6 fatcat:vivhu673mzcxzb3sh6jvjj4edu