A convexity theorem for real projective structures
Geometric Topology
2007-05-29 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0705.3920,
title = {A convexity theorem for real projective structures},
author = {Jaejeong Lee},
journal= {arXiv preprint arXiv:0705.3920},
year = {2007}
}