Journal of the
Korean Mathematical Society JKMS

We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.

Keywords: overdetermined PDE system, prolongation, complete system, involutivity, CR embedding, infinitesimal CR automorphism

MSC numbers: 32F25, 35N10, 58A17