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arXiv · 1812.01086

Centroaffine Duality for Spatial Polygons

Marcos Craizer·Sinesio Pesco
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Abstract

In this paper, we discuss centroaffine geometry of polygons in $3$-space. For a polygon $X$ that is locally convex with respect to an origin together with a transversal vector field $U$, we define the centroaffine dual pair $(Y,V)$ similarly to [6]. We prove that vertices of $(X,U)$ correspond to flattening points for $(Y,V)$ and also that constant curvature polygons are dual to planar polygons. As an application, we give a new proof of a known $4$ flattening points theorem for spatial polygons.

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Marcos Craizer, Sinesio Pesco. 2018-12-03. Centroaffine Duality for Spatial Polygons. https://arxiv.org/abs/1812.01086

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