# Translation surface

From Diffgeom

This article defines a property that makes sense for a surface embedded in , 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 is termed a **translation surface** if it has the following Cartesian equation:

where are smooth functions from open sets in , to .