  We investigate the property of boundary rigidity for the projective
structures associated to torsion-free affine connections on connected analytic
manifolds with boundary. We show that these structures are generically boundary
rigid, meaning that any automorphism of a generic projective structure that
restricts to the identity on the boundary must itself be the identity. However,
and in contrast with what happens for example for conformal structures, we show
that there exist projective structures which are not boundary rigid. We
characterise these non-rigid structures by the vanishing of a certain local
projective invariant of the boundary.
