Flat affine maximal surfaces in \(\mathbb{R}^{4}\)
For nondegenerate immersed surfaces \(\phi: M^2\to \mathbb R^4\), under the equiaffine structure of Nomizu and Vrancken, the definite extremal surfaces (the authors called them maximal surfaces, that is, the mean curvature vanishes identity) with flat induced connection, and the indefinite extremal surfaces (the authors called them also maximal surfaces) with flat induced connection and flat affine metric, are classified.
scientific article; zbMATH DE number 5659736