Mathematica Bohemica, Vol. 143, No. 4, pp. 431-439, 2018

The symmetry reduction of variational integrals, complement

Veronika Chrastinová, Václav Tryhuk

Received October 4, 2017.   Published online April 17, 2018.

Abstract:  Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
Keywords:  Lagrange variational problem; Poincaré-Cartan form; symmetry reduction
Classification MSC:  49S05, 49N99, 70H03
DOI:  10.21136/MB.2018.0111-17

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Affiliations:   Veronika Chrastinová, Brno University of Technology, Faculty of Civil Engineering, Department of Mathematics, Veveři 331/95, 602 00 Brno, Czech Republic, e-mail:; Václav Tryhuk, Brno University of Technology, Faculty of Civil Engineering, AdMaS centre, Purkyňova 139, 612 00 Brno, Czech Republic, e-mail:,

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