Convex real projective structures on closed surfaces are closed. (English) Zbl 0810.57005

Choi, Suhyoung; Goldman, William M.

Proc. Am. Math. Soc. 118, No. 2, 657-661 (1993).

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.

Reviewer: S.Y.Husseini (Madison)

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

Keywords:

space of representations of the fundamental group into \(\text{SL} (3,\mathbb{R})\); deformation space of convex \(RP^ 2\)-structures on a closed surface; Teichmüller component

References:

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