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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.

##### MSC:
 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
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##### References:
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