Affine translation surfaces with constant sectional curvature (Q1581016)

Translation surfaces \(M^2\) in \(\mathbb{R}^4\) are surfaces which can be written locally as a sum of two curves. Using a special transversal plane bundle the authors prove the following two main theorems. Theorem 1.1: The Gaussian curvature of a translation surface is zero iff one of the defining curves is planar. Theorem 1.2: If the Gauss curvature of a translation surface is constant, then it is zero.