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

Abstract

Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists to enrich a plane field, as this is often practised in control theory, by adding brackets of the vector fields tangent to it, and then, look for singular solutions of the obtained distribution. We apply this to the isometry problem of rigid geometric structures.