The marked length spectrum of a projective manifold or orbifold

Details The marked length spectrum of a projective manifold or orbifold The marked length spectrum of a projective manifold or orbifold

2009-12-29

arxiv.org/abs/0912.5341v1

Mathematics

Geometric Topology

16 pages

Scientific paper

A strictly convex real projective orbifold is equipped with a natural Finsler metric called the Hilbert metric. In the case that the projective structure is hyperbolic, the Hilbert metric and the hyperbolic metric coincide. We prove that the marked Hilbert length spectrum determines the projective structure only up to projective duality. A corollary is the existence of non-isometric diffeomorphic strictly convex projective manifolds (and orbifolds) that are isospectral. The corollary follows from work of Goldman and Choi, and Benoist.

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