S. Choi et Wm. Goldman, THE CLASSIFICATION OF REAL PROJECTIVE-STRUCTURES ON COMPACT SURFACES, Bulletin, new series, of the American Mathematical Society, 34(2), 1997, pp. 161-171
Real projective structures (RP2-structures) on compact surfaces are cl
assified. The space of projective equivalence classes of real projecti
ve structures on a closed orientable surface of genus g > 1 is a count
able disjoint union of open cells of dimension 16g - 16. A key idea is
Choi's admissible decomposition of a real projective structure into c
onvex subsurfaces along closed geodesics. The deformation space of con
vex structures forms a connected component in the moduli space of repr
esentations of the fundamental group in PGL(3, R), establishing a conj
ecture of Hitchin.