S. Choi et Wm. Goldman, CONVEX REAL PROJECTIVE-STRUCTURES ON CLOSED SURFACES ARE CLOSED, Proceedings of the American Mathematical Society, 118(2), 1993, pp. 657-661
The deformation space c(SIGMA) of convex RP2- structures on a closed s
urface SIGMA with CHI(SIGMA) < 0 is closed in the space Hom(pi, SL(3,
R))/SL(3, R) of equivalence classes of representations pi1(SIGMA) -->
SL(3, R). Using this fact, we prove Hitchin's conjecture that the cont
ractible ''Teichmuller component'' (Lie groups and Teichmuller space,
preprint) of Hom(pi, SL(3, R))/SL(3, R) precisely equals c(SIGMA).