Properly convex bending of hyperbolic manifolds

  • Samuel A. Ballas

    Florida State University, Tallahassee, USA
  • Ludovic Marquis

    Université de Rennes I, France
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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.

Cite this article

Samuel A. Ballas, Ludovic Marquis, Properly convex bending of hyperbolic manifolds. Groups Geom. Dyn. 14 (2020), no. 2, pp. 653–688

DOI 10.4171/GGD/558