Convex decompositions of real projective surfaces. II: Admissible decompositions. (English) Zbl 0822.53009

[Part I, cf. same journal 40, No. 1, 165-208 (1994; Zbl 0818.53042).]
A real projective surface is a differentiable surface with an atlas of charts to the real projective plane \({\mathbb{R}}{\mathbb{P}}^ 2\) such that transition functions are restrictions of projective automorphisms of \({\mathbb{R}\mathbb{P}}^ 2\). Let \(\Sigma\) be an orientable compact real projective surface with convex boundary and with negative Euler characteristic. Then \(\Sigma\) uniquely decomposes along mutually disjoint imbedded closed projective geodesics into compact subsurfaces that are maximal annuli, trivial annuli, or maximal purely convex real projective surfaces. This is a positive answer to a question by Thurston and Goldman raised around 1977.
Reviewer: S.Choi (Taegu)


53B10 Projective connections


Zbl 0818.53042
Full Text: DOI