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June, 2001 Rigidity and Deformation Spaces of Strictly Convex Real Projective Structures on Compact Manifolds
Inkang Kim
J. Differential Geom. 58(2): 189-218 (June, 2001). DOI: 10.4310/jdg/1090348324

Abstract

In this paper we show that if two strictly convex, compact real projective manifolds have the same marked length spectrum with respect to the Hilbert metric, then they are projectively equivalent. This is a rigidity for Finsler metric with a special geometric structure. Furthermore we prove an analogue of a Hitchin's conjecture for hyperbolic 3-manifolds, namely the deformation space of convex real projective structures on a compact hyperbolic 3-manifold M is a component in the moduli space of PGL(4,ℍ)-representations of π1(M).

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Inkang Kim. "Rigidity and Deformation Spaces of Strictly Convex Real Projective Structures on Compact Manifolds." J. Differential Geom. 58 (2) 189 - 218, June, 2001. https://doi.org/10.4310/jdg/1090348324

Information

Published: June, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1076.53053
MathSciNet: MR1913941
Digital Object Identifier: 10.4310/jdg/1090348324

Rights: Copyright © 2001 Lehigh University

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Vol.58 • No. 2 • June, 2001
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