A characterization of hyperbolic affine flat, affine minimal surfaces in $\mathbb{A}^3$

TL;DR

This paper classifies hyperbolic affine flat, affine minimal surfaces in three-dimensional affine space using Cartan's moving frames, providing a complete set of invariants and new examples.

Contribution

It offers the first complete local classification of these surfaces and constructs new explicit examples using Cartan's method.

Findings

Complete set of local invariants derived

Classification of hyperbolic affine flat, affine minimal surfaces

New explicit examples constructed

Abstract

We investigate the geometric properties of hyperbolic affine flat, affine minimal surfaces in the equiaffine space $\mathbb{A}^3$. We use Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a complete local classification of such surfaces and construct new examples.