Discrete Affine Minimal Surfaces with Indefinite Metric

Details Discrete Affine Minimal Surfaces with Indefinite Metric Discrete Affine Minimal Surfaces with Indefinite Metric

2008-03-10

arxiv.org/abs/0803.1506v3

Mathematics

Differential Geometry

12 pages, 13 figures

Scientific paper

Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that they are critical points of an affine area functional defined on the space of quadrangular discrete surfaces. The construction makes use of asymptotic coordinates and allows defining the discrete analogs of some differential geometric objects, such as the normal and co normal vector fields, the cubic form and the compatibility equations.

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