Geometric integration by parts and Lepage equivalents
arXiv:2010.16135 · doi:10.1016/j.difgeo.2022.101866
Abstract
We compare the integration by parts of contact forms - leading to the definition of the interior Euler operator - with the so-called canonical splittings of variational morphisms. In particular, we discuss the possibility of a generalization of the first method to contact forms of lower degree. We define a suitable Residual operator for this case and, working out an original conjecture by Olga Rossi, we recover the Krupka-Betounes equivalent for first order field theories. A generalization to the second order case is discussed.
37 pages, presentation changed, new results and example added, v3: equations numbering corrected