A convexity theorem for real projective structures

Details A convexity theorem for real projective structures A convexity theorem for real projective structures

2007-05-27

arxiv.org/abs/0705.3920v1

Mathematics

Geometric Topology

61 pages, 19 figures

Scientific paper

Given a finite collection P of convex n-polytopes in RP^n (n>1), we consider a real projective manifold M which is obtained by gluing together the polytopes in P along their facets in such a way that the union of any two adjacent polytopes sharing a common facet is convex. We prove that the real projective structure on M is (1) convex if P contains no triangular polytope, and (2) properly convex if, in addition, P contains a polytope whose dual polytope is thick. Triangular polytopes and polytopes with thick duals are defined as analogues of triangles and polygons with at least five edges, respectively.

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