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The Hilbert-Carathéodory form for parametric multiple integral problems in the calculus of variations. (English) Zbl 1031.53106

The Hilbert 1-form, emphasized by Chern in Finsler geometry, is a special case of the Poincaré-Cartan form of Lagrangian dynamics. One can accomplish this with just a homogeneity condition. The authors show that the Carathéodory form for multiple integral problems can also be specialized in a similar manner. The new Hilbert (called Hilbert-Carathéodory) form is used to derive the Euler-Lagrange equations.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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