The marked length spectrum of a projective manifold or orbifold
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Abstract:
A strictly convex real projective orbifold is equipped with a natural Finsler metric called a 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. This corollary follows from work of Goldman and Choi, and Benoist.References
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Additional Information
- Daryl Cooper
- Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106
- MR Author ID: 239760
- Email: cooper@math.ucsb.edu
- Kelly Delp
- Affiliation: Department of Mathematics, Buffalo State College, Buffalo, New York 14222
- Email: kelly.delp@gmail.com
- Received by editor(s): July 1, 2009
- Received by editor(s) in revised form: December 12, 2009, and December 29, 2009
- Published electronically: April 6, 2010
- Communicated by: Richard A. Wentworth
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3361-3376
- MSC (2010): Primary 57N16
- DOI: https://doi.org/10.1090/S0002-9939-10-10359-1
- MathSciNet review: 2653965