The Gauss image of flat surfaces in \(R^ 4\) (Q1074119)

Let M be a flat surface in \({\mathbb{R}}^ 4\) with flat normal connection. Then the image of the Gauss map \(G: M\to G(2,4)=S^ 2\times S^ 2\) is contained in the Riemannian product of two curves in \(S^ 2\). If the latter are great circles, then M is a Riemannian product of planar curves.