Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 1, pp. 153-170 (2015)

Variational theory on Grassmann fibrations: Examples

Zbynek Urban and Demeter Krupka

University of Hradec Králové and Lepage Research Institute

Abstract: Simple examples of variational functionals on Grassmann fibrations are analysed on the basis of the Hilbert form. The Lagrange, Euler-Lagrange, and Noether classes, characterizing the functionals, their extremals and invariance properties are discussed. The relationship of equations for extremals and conservation law equations is established; in the examples the system of Euler-Lagrange equations turns out to be equivalent with the system of conservation law equations.

Classification (MSC2000): 58E30; 58D19, 53C40, 58A20

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