The marked length spectrum of a projective manifold or orbifold

2009/12/29 by Daryl Cooper, Cooper, Daryl, Kelly Delp +1 · 2 citations
Mathematics · Physics and Astronomy · #57M50 #57N16 #58H15 #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0912.5341

openalex publication_date 2009/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Primitive stability and the Q-conditions for the rank two free group in hyperbolic d-space
• Simple Length Rigidity for Hitchin Representations

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