Mathematics – Geometric Topology
Scientific paper
2010-04-21
Mathematics
Geometric Topology
Scientific paper
We build examples of properly convex projective manifold $\Omega/ \Gamma$ which have finite volume, are not compact, nor hyperbolic in every dimension $n \geqslant 2$. On the way, we build Zariski-dense discrete subgroups of $\SL_{n+1}(\R)$ which are not lattice, nor Schottky groups. Moreover, the open properly convex set $\Omega$ is strictly-convex, even Gromov-hyperbolic. Nous construisons des exemples de vari\'et\'es projectives $\Omega/ \Gamma$ proprement convexes de volume fini, non hyperbolique, non compacte en toute dimension $n \geqslant 2$. Ceci nous permet au passage de construire des groupes discrets Zariski-dense de $\SL_{n+1}(\R)$ qui ne sont ni des r\'eseaux de $\SL_{n+1}(\R)$, ni des groupes de Schottky. De plus, l'ouvert proprement convexe $\Omega$ est strictement convexe, m\^eme Gromov-hyperbolique.
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