Geometry of Linear Differential Systems Towards Contact Geometry of Second Order

Abstract

This is a lecture note on the geometry of linear differential systems. By a (linear) differential system (or Pfaffian system) (M, D), we mean a subbundle D of the tangent bundle T(M) of a manifold M. Locally D is defined by 1-forms w 1,...,w s such that w 1Λ⋯Λw s ≠0 at each point , where r is the rank of D and r + s = dim M; D={ω1=⋯=ωs=0}. D = \{ \omega _1 = \cdots = \omega _s = 0\} .