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On the Carathéodory Form in Higher-Order Variational Field Theory

Department of Mathematics, Faculty of Civil Engineering, VŠB—Technical University of Ostrava, Ludvíka Podéště 1875/17, 708 33 Ostrava, Czech Republic
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Academic Editor: Wei-Shih Du
Symmetry 2021, 13(5), 800; https://doi.org/10.3390/sym13050800
Received: 16 April 2021 / Revised: 28 April 2021 / Accepted: 30 April 2021 / Published: 4 May 2021
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
The Carathéodory form of the calculus of variations belongs to the class of Lepage equivalents of first-order Lagrangians in field theory. Here, this equivalent is generalized for second- and higher-order Lagrangians by means of intrinsic geometric operations applied to the well-known Poincaré–Cartan form and principal component of Lepage forms, respectively. For second-order theory, our definition coincides with the previous result obtained by Crampin and Saunders in a different way. The Carathéodory equivalent of the Hilbert Lagrangian in general relativity is discussed. View Full-Text
Keywords: Carathéodory form; Poincaré–Cartan form; Lepage equivalent; fibered manifold; variational field theory Carathéodory form; Poincaré–Cartan form; Lepage equivalent; fibered manifold; variational field theory
MDPI and ACS Style

Urban, Z.; Volná, J. On the Carathéodory Form in Higher-Order Variational Field Theory. Symmetry 2021, 13, 800. https://doi.org/10.3390/sym13050800

AMA Style

Urban Z, Volná J. On the Carathéodory Form in Higher-Order Variational Field Theory. Symmetry. 2021; 13(5):800. https://doi.org/10.3390/sym13050800

Chicago/Turabian Style

Urban, Zbyněk, and Jana Volná. 2021. "On the Carathéodory Form in Higher-Order Variational Field Theory" Symmetry 13, no. 5: 800. https://doi.org/10.3390/sym13050800

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