Titlebook: Introduction to Global Variational Geometry; Demeter Krupka Book 2015 Atlantis Press and the author 2015 conservation law.inverse problem.

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Variational Structures,d . with ., it is proved that the form . in the variational functional . may be chosen in such a way that the Cartan’s formula for. becomes a geometric version of the classical .. A structure theorem implies that for different underlying manifold structures and order of their jet prolongations, the

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Invariant Variational Structures,extension of the classical coordinate concepts and methods to topologically nontrivial fibred manifolds that cannot be covered by a single chart. The geometric coordinate-free structure of the infinitesimal first variation formula leads in several consequences, such as the geometric invariance crite

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Indecisive

Formal Divergence Equations,ted “ordinary” divergence equation along any section of the underlying fibered manifold. The notable fact is that the solutions of formal divergence equations of order . are in one–one correspondence with a class of differential forms on the .-st jet prolongation of the underlying fibered manifold, defined by the exterior derivative operator.

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Examples: Natural Lagrange Structures,re the . We give a manifold interpretation of this functional and show that its . Lagrangian, the ., possesses a global . equivalent. The Lagrangian used by Hilbert is an example of a . of a metric field (and its first and second derivatives). Further examples with similar properties, belonging to the class of ., are also considered.

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