We examine three invariants for exact loops of Lagrangian submanifolds that are modelled on invariants introduced by Leonid Polterovich for loops of Hamiltonian symplectomorphisms. One of these is the minimal Hofer length in a given Hamiltonian isotopy class. We determine the exact values of these invariants for loops of projective Lagrangian planes. The proof uses the Gromov invariants of an associated symplectic fibration over the 2-disc with a Lagrangian subbundle over the boundary. The last two chapters concern different topics and can be read completely independently.