Fully integrable Pfaffian systems (Q1062323)

It is well known that a Pfaffian system may be fully integrable at some points and not at others. It is a fundamental problem to determine the exact conditions of full integrability at a prescribed point q. In the paper under review the author gives such conditions for a class of \(C^{\infty}\)-Pfaffian systems enjoying a certain finiteness property. In particular he obtains a complete solution of the full integrability problem for all real-analytic systems.