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arXiv · 0904.2489

Entropies of compact strictly convex projective manifolds

Mickaël Crampon
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Abstract

Let M be a compact manifold of dimension n with a strictly convex projective structure. We consider the geodesic flow of the Hilbert metric on it, which is known to be Anosov. We prove that its topological entropy is less than n-1, with equality if and only if the structure is Riemannian, that is hyperbolic. As a corollary, we get that the volume entropy of a divisible strictly convex set is less than n-1, with equality if and only if it is an ellipsoid.

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Mickaël Crampon. 2009-04-16. Entropies of compact strictly convex projective manifolds. https://arxiv.org/abs/0904.2489

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