INVARIANT DIFFERENTIAL SYSTEMS AND CANONICAL FORMS OF E. CARTAN
Abstract
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 Cartan's contributions to infinite continuous pseudo groups. The purpose of this paper is to develop parts of the older theory of Lie and Vessiot in Cartan's con text. The essential role played by Cartan's canonical forms in determining invariant systems is demonstrated. Automorphic systems can be completely described in a manner similar to Lie's, but Cartan's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1963
- Accession Number
- AD0404457
Entities
People
- H. H. Johnson
Organizations
- University of Washington