In this paper we show that bending a finite volume hyperbolic -manifold along a totally geodesic hypersurface results in a properly convex projective structure on 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 there are examples finite volume, but non-compact, properly convex -manifolds. Furthermore, we show that the examples can be chosen to be either strictly convex or non-strictly convex.
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Samuel A. Ballas, Ludovic Marquis, Properly convex bending of hyperbolic manifolds. Groups Geom. Dyn. 14 (2020), no. 2, pp. 653–688DOI 10.4171/GGD/558