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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zbyněk Urban & Jana Volná, 2022. "The Fundamental Lepage Form in Two Independent Variables: A Generalization Using Order-Reducibility," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1211-:d:789031
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