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Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric

Marcos Craizer
Arxiv ID: 0805.2060Last updated: 1/15/2020
Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine area, mean curvature, normal and co-normal vector fields and cubic form, and they are related by structural and compatibility equations. We consider also the particular cases of affine minimal surfaces and affine spheres.

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