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Journal Articles Groups, Geometry, and Dynamics Year : 2020

Properly Convex Bending of Hyperbolic Manifolds

Abstract

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.
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Dates and versions

hal-01363922 , version 1 (12-09-2016)
hal-01363922 , version 2 (08-04-2020)

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Samuel A. Ballas, Ludovic Marquis. Properly Convex Bending of Hyperbolic Manifolds. Groups, Geometry, and Dynamics, 2020, 14 (2), pp. 653-688. ⟨hal-01363922v2⟩
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