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

Geometric problems are usually formulated by means of (exterior) differenti al systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks fur regular solutions. Here we ad opt a dual approach, which consists of enriching a plane field, as this is often practised in control theory, by adding brackets of the vector fields tangent to it and, then, looking for singular solutions of the obtained dis tribution. We apply this to the isometry problem of rigid geometric structu res.