We investigate the reduction process of a k-symplectic field theory whose
Lagrangian is invariant under a symmetry group. We give explicit coordinate
expressions of the resulting reduced partial differential equations, the
so-called Lagrange-Poincare field equations. We discuss two issues about
reconstructing a solution from a given solution of the reduced equations. The
first one is an interpretation of the integrability conditions, in terms of the
curvatures of some connections. The second includes the introduction of the
concept of a k-connection to provide a reconstruction method. We show that an
invariant Lagrangian, under suitable regularity conditions, defines a
`mechanical' k-connection.Comment: 37 page
