Derivations of differential forms on jet bundles

Summary The theory of derivations of differential forms, originally formulated by Frölicher and Nijenhuis 2], is generalized to include derivations which connect differential forms on two different manifolds. This generalized theory is then used to analyze derivations of direct limits of exterior algebras of forms on jet bundles. Such derivations have found applications in the analysis of Lie equations 3], 4] and in the inverse problem of the calculus of variations 6], 7], 8], 9].

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Résumé On présente une généralization de la théorie des dérivations des formes extérieures, formulée par Frölicher et Nijenhuis 2], au cas des dérivations qui relient les formes extérieurs sur deux variétés différentes. On utilize ensuite cette théorie généralizée pour étudier les dérivations des limites directes des algèbres des formes extérieures sur les fibrés des jets. Ces dérivations ont été appliquées dans l'analyse des équations de Lie 3], 4] et dans le problème inverse du calcul des variations 6], 7], 8], 9].

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This work is a part of a program conducted jointly with ProfessorBenenti at Istituto di Fisica Matematica «J. L. Lagrange» of Torino. The authors are greatly indebted to the Director of the Institute Professor D.Galletto for his interest and encouragement.This work has been supported by Gruppo Nazionale per la Fisica Matematica del Consiglio Nazionale delle Ricerche.