Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric

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