Translation surface

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This article defines a property that makes sense for a surface embedded in \R^3, viz three-dimensional Euclidean space. The property is invariant under orthogonal transformations and scaling, i.e., under all similarity transformations.
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A surface in \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 \R, to \R.