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

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

1998-03-11

arxiv.org/abs/math/9803038v1

Mathematics

Differential Geometry

14 pages, LaTex

Scientific paper

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.

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