Strongly dense representations of hyperbolic 3-manifold groups

We provide the first examples of strongly dense representations of a hyperbolic 3-manifold group into S L ( 4 , R ) SL(4,R) and S U ( 3 , 1 ) SU(3,1) i.e. representations where every pair of non-commuting elements has Zariski dense image. Our examples are holonomy representations arising from projective deformations of its hyperbolic structure. As a corollary, we get that S L ( 4 , R ) SL(4,R) has non-Hitchin strongly dense surface subgroups.