## Convex decompositions of real projective surfaces. III: For closed or nonorientable surfaces.(English)Zbl 0958.53022

From the introduction: The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $$\mathbb{R} P^2$$ such that the transition functions are restrictions of projective automorphisms of $$\mathbb{R} P^2$$. Since such an atlas lifts projective geometry on $$\mathbb{R} P^2$$ to the surface locally and consistently, one can study the global projective geometry of surfaces.
This paper is the last of a series of papers [J. Differ. Geom. 40, 165-208 (1994; Zbl 0818.53042) and 239-283 (1994; Zbl 0822.53009)]. With this paper, we get a satisfactory classification of all real projective structures on surfaces [see the author and W. Goldman, Bull. Am. Math. Soc., New Ser. 34, 161-171 (1997; Zbl 0866.57001)]. This final paper shows that a nonorientable real projective surface also has an admissible decomposition and a closed real projective surface decomposes into pieces that are convex real projective surfaces or $$\pi$$-Möbius bands.

### MSC:

 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 57M50 General geometric structures on low-dimensional manifolds 53A20 Projective differential geometry

### Citations:

Zbl 0818.53042; Zbl 0822.53009; Zbl 0866.57001