Translation surface

This article defines a property that makes sense for a surface embedded in

${\mathbb{R}}^3$

, viz three-dimensional Euclidean space. The property is invariant under orthogonal transformations and scaling, i.e., under all similarity transformations.
View other such properties

Definition

A surface in ${\mathbb{R}}^3$ is termed a translation surface if it has the following Cartesian equation:

$z=f(x)+g(y)$

where $f,g$ are smooth functions from open sets in $\mathbb{R}$, to $\mathbb{R}$.