Geodesic
A new infinite order formulation of variational sequences
Archivum mathematicum, Tome 34 (1998) no. 4, pp. 483-504
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The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition and in the computations. We think that our infinite order approach could be easily applied in concrete situations, due to the conceptual simplicity of the scheme.
The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition and in the computations. We think that our infinite order approach could be easily applied in concrete situations, due to the conceptual simplicity of the scheme.
Classification : 49J45, 58A12, 58A20, 58E30, 58J10
Keywords: fibred manifold; jet space; infinite order jet space; variational bicomplex; variational sequence 483504 
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Vitolo, Raffaele. A new infinite order formulation of variational sequences. Archivum mathematicum, Tome 34 (1998) no. 4, pp. 483-504. http://geodesic.mathdoc.fr/item/ARM_1998_34_4_a7/

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