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Geometric problems are usually formulated by means of (exterior) differentialsystems. In this theory, one enriches the system by adding algebraic anddifferential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists to enrich a plane field, as thisis often practised in control theory, by adding brackets of the vector fieldstangent to it, and then, look for singular solutions of the obtaineddistribution. We apply this to the isometry problem of rigid geometricstructures.

On Gromov's theory of rigid transformation groups: a dual approach