A curvature-ellipse-based Monge normal form of a regular surface in $\mathbb{R}^4$ and its applications

We study a Monge normal form of a surface in $\mathbb{R}^4$ based on the principal axes of its curvature ellipse. The curvature-ellipse-based Monge normal form is obtained using only Euclidean motions of the ambient space and local reparameterizations of the surface, and preserves the Euclidean inva