Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric
Differential Geometry
2020-01-15 v2
Abstract
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.
Cite
@article{arxiv.0805.2060,
title = {Asymptotic Nets and Discrete Affine Surfaces with Indefinite Metric},
author = {Marcos Craizer},
journal= {arXiv preprint arXiv:0805.2060},
year = {2020}
}
Comments
The paper will be re-written in a different context