Properly convex bending of hyperbolic manifolds

Samuel A. Ballas; Ludovic Marquis

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arXiv · 1609.03046

Properly convex bending of hyperbolic manifolds

Samuel A. Ballas·Ludovic Marquis

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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 $d\geq 3$ 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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BibTeX RIS

Samuel A. Ballas, Ludovic Marquis. 2016-09-10. Properly convex bending of hyperbolic manifolds. https://arxiv.org/abs/1609.03046

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