Properly convex bending of hyperbolic manifolds

Samuel A. Ballas, Ludovic Marquis

In this paper we show that bending a finite volume hyperbolic \$d\$-manifold \$M\$ along a totally geodesic hypersurface \$\Sigma\$ results in a properly convex projective structure on \$M\$ with finite volume. We also discuss various geometric properties of bent manifolds and algebraic properties of their fundamental groups. We then use this result to show in each dimension \$d\ge 3\$ there are examples finite volume, but non-compact, properly convex \$d\$-manifolds. Furthermore, we show that the examples can be chosen to be either strictly convex of non-strictly convex.