Abstract:
Here some ideas about reduction for principal bundles are
presented.
It is known that Classical Field theories of first order can
be
formulated as Lagrangian submanifolds
of premultisymplectic manifolds
through
a particular Tulczyjew's Triple. In the case, the
Classical Field
theories
is a G-principal bundle a new triple and new Lagrangian
submanifolds related with the previous
ones are obtained to formulated
the
Euler-Poincare and the Hamilton-Poincare equations when the
Lagrangian and the Hamiltonian density
are G-invariant.