## 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.

### MSC:

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

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