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The marked length spectrum of a projective manifold or orbifold

Authors: Daryl Cooper and Kelly Delp
Journal: Proc. Amer. Math. Soc. 138 (2010), 3361-3376
MSC (2010): Primary 57N16
Published electronically: April 6, 2010
MathSciNet review: 2653965
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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.

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Additional Information

Daryl Cooper
Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106

Kelly Delp
Affiliation: Department of Mathematics, Buffalo State College, Buffalo, New York 14222

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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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