Groups, Geometry, and Dynamics
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Published online: 2020-06-24
Properly convex bending of hyperbolic manifoldsSamuel A. Ballas and Ludovic Marquis (1) Florida State University, Tallahassee, USA
(2) Université de Rennes I, France
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 $d\geqslant 3$ 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 or non-strictly convex.
Keywords: Projective geometry, convex projective structures, bending
Ballas Samuel, Marquis Ludovic: Properly convex bending of hyperbolic manifolds. Groups Geom. Dyn. 14 (2020), 653-688. doi: 10.4171/GGD/558