Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles. (English) Zbl 1249.53029

Summary: Let \(\mu \: FX \to X\) be a principal bundle of frames with the structure group  \(\text{Gl}_{n}(\mathbb R)\). It is shown that the variational problem, defined by \(\text{Gl}_{n}(\mathbb R)\)-invariant Lagrangian on \(J^{r} FX\), can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.


53C05 Connections (general theory)
53C10 \(G\)-structures
58A20 Jets in global analysis
58E30 Variational principles in infinite-dimensional spaces
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