Let $p\geq 2$ and $q\geq 1$ be any integers, and let $\mathbb{H}^{p,q}$ be the pseudo-Riemannian hyperbolic space of signature $(p,q)$ . We prove that if $\Gamma $ is the fundamental group of a closed aspherical $p$ -manifold, then the set of representations of $\Gamma $ to ${\mathrm{PO}}(p,q+1)$ which are convex cocompact in $\mathbb{H}^{p,q}$ is a union of connected components of ${\mathrm{Hom}}(\Gamma ,{\mathrm{PO}}(p,q+1))$ . More generally, we show that if $\Gamma $ is any finitely generated group with no infinite nilpotent normal subgroups and with virtual cohomological dimension $p$ , then the set of injective and discrete representations of $\Gamma $ to ${\mathrm{PO}}(p,q+1)$ preserving a non-degenerate non-positive $(p-1)$ -sphere in the boundary of $\mathbb{H}^{p,q}$ is a union of connected components of ${\mathrm{Hom}}(\Gamma ,{\mathrm{PO}}(p,q+1))$ . This gives new examples of higher-dimensional higher-rank Teichmüller spaces.
