Fully integrable Pfaffian systems. (English) Zbl 0572.58001

Freeman, Michael

Ann. Math. (2) 119, 465-510 (1984).

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.

Reviewer: M.Puta

MSC:

58A10

Differential forms in global analysis

Keywords:

fully integrable Pfaffian systems; differential forms of degree 1, integral manifold; real-analytic systems