JournalsggdVol. 14, No. 2pp. 653–688

Properly convex bending of hyperbolic manifolds

  • Samuel A. Ballas

    Florida State University, Tallahassee, USA
  • Ludovic Marquis

    Université de Rennes I, France
Properly convex bending of hyperbolic manifolds cover
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Abstract

In this paper we show that bending a finite volume hyperbolic dd-manifold MM along a totally geodesic hypersurface Σ\Sigma results in a properly convex projective structure on MM 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 d3d\geqslant 3 there are examples finite volume, but non-compact, properly convex dd-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