# Invariant variational problems on principal bundles and conservation laws

## Ján Brajerčík

Address: Department of Physics, Mathematics and Technology, University of Prešov, Ul. 17. novembra 1, 081 16 Prešov, Slovakia

E-mail: brajerci@unipo.sk

Abstract: In this work, we consider variational problems defined by $G$-invariant Lagrangians on the $r$-jet prolongation of a principal bundle $P$, where $G$ is the structure group of $P$. These problems can be also considered as defined on the associated bundle of the $r$-th order connections. The correspondence between the Euler-Lagrange equations for these variational problems and conservation laws is discussed.

AMSclassification: primary 49S05; secondary 58A10, 58A20, 49Q99.

Keywords: principal bundle, variational principle, invariant Lagrangian, Euler-Lagrange equations, Noether’s current, conservation law.