Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Some ideas about reduction for principal bundles arepresented. It is known that Classical Field theories of first order canbe formulated as Lagrangian submanifolds of premultisymplectic manifoldsthrough a particular Tulczyjew's Triple. In the case, the Classical Fieldtheories is a G-principal bundle a new triple and new Lagrangiansubmanifolds related with the previous ones are obtained to formulatedthe Euler-Poincare and the Hamilton-Poincare equations when theLagrangian and the Hamiltonian density are G-invariant.