2004/06/11 by Peter J. Vassiliou, Vassiliou, Peter J. · 1 citation
Mathematics · #34H05 #58J60 #93B18 #93B27 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:34H05 #msc:58J60 #msc:93B18 #msc:93B27
paper · pdf · doi:10.48550/arxiv.math/0406234
23 pages
openalex publication_date 2004/06/11 · arxiv created 2004/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \CV be a vector field distribution on manifold M. We give an efficient algorithm for the construction of local coordinates on M such that \CV may be locally expressed as some partial prolongation of the contact distribution \Cal C(1)q, on the first order jet bundle of maps from \Bbb R to \Bbb Rq, q≥ 1. It is proven that if \CV is locally equivalent to a partial prolongation of \Cal C(1)q then the explicit construction of contact coordinates algorithmically depends upon the determination of certain first integrals in a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on M. The number of these first integrals that must be computed satisfies a natural minimality criterion. These results therefore provide a full and constructive generalisation of the classical Goursat normal form from the theory of exterior differential systems.