INVARIANT DIFFERENTIAL SYSTEMS AND CANONICAL FORMS OF E. CARTAN
WASHINGTON UNIV SEATTLE
Pagination or Media Count:
One of the early applications of continuous transformation groups and pseudo groups was to invariant systems of ordinary and partial differential equations. Much of this work was done by S. Lie and E. Vessiot before Cartans contributions to infinite continuous pseudo groups. The purpose of this paper is to develop parts of the older theory of Lie and Vessiot in Cartans con text. The essential role played by Cartans canonical forms in determining invariant systems is demonstrated. Automorphic systems can be completely described in a manner similar to Lies, but Cartans involutiveness together with an additional hypothesis yield more complete results than in the older theory. Also, following Cartan the theory takes a coordinate-free form. Definitions will be those of M. Kuranishi. It is assumed that manifolds, functions, and forms are real and infinitely differentiable.
- Theoretical Mathematics