A convexity theorem for real projective structures

Jaejeong Lee

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arXiv · 0705.3920

A convexity theorem for real projective structures

Jaejeong Lee

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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.

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BibTeX RIS

Jaejeong Lee. 2007-05-27. A convexity theorem for real projective structures. https://arxiv.org/abs/0705.3920

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