  To a hyperbolic manifold one can associate a canonical projective structure
and ask whether it can be deformed or not. In a cusped manifold, one can ask
about the existence of deformations that are trivial on the boundary. We prove
that if the canonical projective structure of a cusped manifold is
infinitesimally projectively rigid relative to the boundary, then infinitely
many Dehn fillings are projectively rigid. We analyze in more detail the figure
eight knot and the Withehead link exteriors, for which we can give explicit
infinite families of slopes with projectively rigid Dehn fillings.
