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.

PaperStudio AI Chat

I'm your research assistant! Ask me anything about this paper.

Related papers

Commercial Disclosure
© 2023 Paper Studio™. All Rights Reserved.