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Projective structures of elliptic differential operators

Published online by Cambridge University Press:  22 January 2016

Kazushige Ueno
Kazushige Ueno*
Affiliation:
Tokyo University of Fisheries, Minato-ku, Tokyo 108, Japan
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In the study of differential equations from the standpoint of the automorphism pseudogroups, the differential invariants of the pseudogroups play an important role.

A general study of pseudogroups and their differential invariants originated with Sophus Lie. He applied his study to the classification of ordinary and partial differential equations. So as to study differential equations from his point of view, it is very important to write the given differential equation by the differential invariants of the automorphism pseudogroup. That is to say, the geometric structure of a differential equation is contained in the expression of the equation by its differential invariants.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 99 , September 1985 , pp. 111 - 130
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Singer, I. M. and Sternberg, S., The infinite groups of Lie and Cartan, J. Analyse Math., 15 (1965), 1–114.Google Scholar
[ 2 ] Ueno, K., Existence and equivalence theorems of automorphic systems, Publ. RIMS, Kyoto Univ., 11 (1976), 461–482.Google Scholar