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Equivalence of degenerate Lagrangians of higher order. (English) Zbl 0810.58010

Janyška, Josef (ed.) et al., Differential geometry and its applications. International conference, Brno, Czechoslovakia, 27 Aug. - 2 Sept. 1989. Singapore: World Scientific. 255-264 (1990).
Having introduced some basic notions related to higher order tangent bundles, higher order Lagrangians are next defined. To put it simply, higher order Lagrangians, being real functions on \(T^ k Q\), where \(Q\) is a manifold, involve higher order derivatives. Such Lagrangians are studied from the point of view of properly defined equivalence, geometrical equivalence and gauge equivalence. A simple example of two different Lagrangians characterizing the harmonic oscillator equation illustrates the general considerations. The paper may be of interest to specialists in the calculus of variations on manifolds.
For the entire collection see [Zbl 0777.00040].

MSC:

58E99 Variational problems in infinite-dimensional spaces
49Q99 Manifolds and measure-geometric topics
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