On complete maximal submanifolds in pseudo-hyperbolic space

We provide a full classification of complete maximal $p$-dimensional spacelike submanifolds in the pseudo-hyperbolic space ${\mathbf{H}}^{p,q}$, and we study its applications to Teichmüller theory and to the theory of Anosov representations of hyperbolic groups in $\mathsf{P}\mathsf{O}(p,q+1)$.