A convexity theorem for real projective structures
نویسنده
چکیده
Given a finite collection P of convex n-polytopes in RP (n ≥ 2), 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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تاریخ انتشار 2008