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

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.

15 pages