Symmetries in Lagrangian Field Theory

By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first order jet bundles $J^1\pi$ of a fiber bundle $\pi :E\to {\mathbb{R}}^k$ where ${\mathbb{R}}^k$ is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether Theorem is proved.