Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric

Details Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric

2008-05-14

arxiv.org/abs/0805.2060v1

Mathematics

Differential Geometry

13 pages, 2 figures

Scientific paper

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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