A new infinite order formulation of variational sequences. (English) Zbl 0970.58002

The author presents a new approach to the variational bicomplex on the infinite jet prolongation of a fibred manifold. In this approach, which is based on the theory of variational sequences on finite order jet prolongations due to D. Krupka, the information related to the order of jets is lost, but a considerable simplification both in the exposition and in computations is obtained. The author also deduces several interesting geometric results related with the second variational formula.


58A12 de Rham theory in global analysis
58A20 Jets in global analysis
58E30 Variational principles in infinite-dimensional spaces
58J10 Differential complexes
Full Text: EuDML