# Properly Convex Bending of Hyperbolic Manifolds

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1 FSU Mathematics - Department of Mathematics Tallahassee, FL 2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Keywords : Hilbert geome Hyperbolic manifold

Autor: Samuel A. Ballas - Ludovic Marquis -

Fuente: https://hal.archives-ouvertes.fr/

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