The Fundamental Lepage Form in Two Independent Variables: A Generalization Using Order-Reducibility

Zbyněk Urban and Jana Volná
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Zbyněk Urban: Department of Mathematics, Faculty of Civil Engineering, VŠB-Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 33 Ostrava, Czech Republic
Jana Volná: Department of Mathematics, Faculty of Civil Engineering, VŠB-Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 33 Ostrava, Czech Republic

Mathematics, 2022, vol. 10, issue 8, 1-14

Abstract: A second-order generalization of the fundamental Lepage form of geometric calculus of variations over fibered manifolds with 2-dimensional base is described by means of insisting on (i) an equivalence relation “Lepage differential 2-form is closed if and only if the associated Lagrangian is trivial” and (ii) the principal component of Lepage form, extending the well-known Poincaré–Cartan form, preserving order prescribed by a given Lagrangian. This approach completes several attempts of finding a Lepage equivalent of a second-order Lagrangian possessing condition (i), which is well-known for first-order Lagrangians in field theory due to Krupka and Betounes.

Keywords: Lagrangian; Lepage equivalent; Poincaré–Cartan form; fundamental form; calculus of variations; field theory; jet; fibered manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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