Projective Anosov representations, convex cocompact actions, and rigidity

In this paper we show that many projective Anosov representations act convex cocompactly on some properly domain in real space. particular, if a non-elementary word hyperbolic group is not commensurable to non-trivial free product or the fundamental of closed surface, then any representation acts We also preserves domain, it (possibly different) domain. give three applications. First, into general semisimple Lie groups can be defined terms existence cocompact action space (which depends and parabolic subgroup). Next, prove rigidity result involving Hilbert entropy representation. Finally, which shows image boundary map associated rarely $C^2$ submanifold This final applies Hitchin representations.