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Convex real projective structures on closed surfaces are closed. (English) Zbl 0810.57005
The authors show that the deformation space of convex \(RP^ 2\)- structures on a closed surface \(\sigma\), with \(\chi(\sigma) < 0\), is a closed subspace of the space of the equivalence classes of representations \(\pi \to \text{SL} (3,R)\). As a consequence, they show that it coincides with the Teichmüller component, as conjectured by Hitchin.

57M50 General geometric structures on low-dimensional manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
53A20 Projective differential geometry
58D27 Moduli problems for differential geometric structures
Full Text: DOI
[1] S. Choi, Real projective surfaces, Doctoral dissertation, Princeton Univ., 1988.
[2] -, Compact \( \mathbb{R}{{\mathbf{P}}^2}\)-surfaces with convex boundary I: \( \pi \)-annuli and convexity (submitted).
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[4] William M. Goldman, Topological components of spaces of representations, Invent. Math. 93 (1988), no. 3, 557 – 607. · Zbl 0655.57019 · doi:10.1007/BF01410200 · doi.org
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[8] N. H. Kuiper, On convex locally-projective spaces, Convegno Internazionale di Geometria Differenziale, Italia, 1953, Edizioni Cremonese, Roma, 1954, pp. 200 – 213.
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