×

Pfaffian systems in involution. (English) Zbl 0677.58005

Differential geometry and differential equations, Proc. Symp., Changchun/China 1982, 233-256 (1986).
[For the entire collection see Zbl 0646.00007.]
In this paper an excellent treatment of Pfaffian systems in involution is given. The Cauchy-Kowalewsky theorem, which concerns existence of solutions of partial differential equations, does not apply to “over- determined systems” in which the number of equations is greater than the number of unknown functions.
An important class of such systems, the involutive systems, is covered by the Cartan-Kähler theorem which is a natural generalization of the Cauchy-Kowalewsky theorem. Pfaffian systems in involution, the subject of this paper, are differential systems and are of great importance in geometry and physics. Examples from function theory and mathematical physics are given. The interested reader should see “Exterior differential systems”, R. Bryant, S. Chern and P. A. Griffiths, Proc. 1980 Beijing Symp. Vol. 1, 219-338 (1982; Zbl 0516.58003).
Reviewer: A.Stone

MSC:

58A17 Pfaffian systems