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On a Theorem Concerning the Prolongation of a Differential System

Published online by Cambridge University Press:  22 January 2016

Yozô Matsushima
Yozô Matsushima*
Affiliation:
Mathematical Institute, Nagoya University
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E. Cartan has proved that the prolonged system of a Pfaffian system in involution is also in involution. But he has treated only the case of a Pfaffian system of some special type. On the other hand in his book [3] he has reduced the solution of any differential system to the solution of a Pfaffian system of the type mentioned above, and this reduction is precisely the method of the prolongation of a differential system. Therefore it seems to be disirable to establish the above mentioned theorem in the case of an arbitrary differential system.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 1 - 16
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Bourbaki, N., Algèbre, Chapiter II, Algèbre Linéaire, Chapitre Hi, Algèbre Multilinéaire, 1948.Google Scholar
[2] Cartan, E., Sur la structure des groupes infinis de transformations, Annales École normale sup., 21, 1904.Google Scholar
[3] Cartan, E., Les systèmes différentiels extérieurs et leurs applications géometriques, Paris, 1945.Google Scholar
[4] Chevalley, C. Theory of Lie Groups. I, Princeton, 1946.Google Scholar
[5] Kähler, E., Einführung in die Theorie der Systeme von Differentialgleichungen, Hamburger Math. Einzelschrifte, 16, 1934.Google Scholar
[6] Schouten, J. A. and van der Kulk, W., Pfaff’s problem and its generalizations, Oxford, 1949.Google Scholar