Loops of Lagrangian submanifolds and pseudoholomorphic discs

We examine three invariants of exact loops of Lagrangian submanifolds that are modelled on invariants introduced by Polterovich for loops of Hamiltoni an symplectomorphisms. One of these is the minimal Hofer length in a given Hamiltonian isotopy class. We determine the exact values of these invariant s for loops of projective Lagrangian planes. The proof uses the Gromov inva riants of an associated symplectic fibration over the 2-disc with a Lagrang ian subbundle over the boundary.