Properly Convex Bending of Hyperbolic ManifoldsReport as inadecuate




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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





Author: Samuel A. Ballas - Ludovic Marquis -

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



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