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.