On complexes related with calculus of variations

Details On complexes related with calculus of variations On complexes related with calculus of variations

2001-05-27

arxiv.org/abs/math/0105223v1

J.Geom.Phys. 44 (2002) 221-250

Mathematics

Differential Geometry

LaTeX2e, 36 pages

Scientific paper

10.1016/S0393-0440(02)00075-X

We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a particular new class of forms. We establish relation of the complex of variational derivatives and the variational complex. Certain calculus of Lagrangians of multidimensional paths is developed. It is shown how covariant Lagrangians of higher order can be used to represent characteristic classes.

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