Description |
In my talk, I will explain how covex projective geometry is a generalisation of hyperbolic geometry. A convex projective manifold M is the quotient of a properly open convex $\omega$ set by a discrete group of projective transformation Gamma. The basic example of such manifold is the quotient of the hyperbolic space by a discrete group of isometry. This kind of manifold carry a natural measure. A lot of people have studied the case where the manifold M is compact. I will explain what is known when the dimension of M is 2 and how to construct such a manifold when
$\omega$ is not the hyperbolic space. This will
lead us, to the construction of discrete subgroup
of $SL_n+1(\mathbb (R)$.
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