Examples of strictly convex projective manifolds of finite volume in arbitrary dimension (Q353408)

Summary: We construct examples of properly convex projective manifolds \(\Omega \Gamma\) of finite volume that are non-hyperbolic and non-compact in all dimensions \(n\geq 2\). This allows us along the way to construct Zariski-dense discrete subgroups \(\Gamma\) of \(\mathrm{SL}_{n+1}(\mathbb R)\) that are neither lattices of \(\mathrm{SL}_{n+1}(\mathbb R)\) nor Schottky groups. Moreover, the properly convex domains \(\Omega\) thus constructed are strictly convex, even Gromov-hyperbolic. Finally, we give a sufficient condition for the gluing of convex projective manifolds with totally geodesic boundary to be a convex projective manifold.