Reconstruction of a two-dimensional surface in \(n\)-dimensional Euclidean space from its Grassmann image (Q1059285)

The author gives necessary and sufficient conditions for a two-surface \(\Gamma^ 2\) in a Grassmann manifold \(G_{n-2,n}\) to be the image of some two-surface \(F^ 2\) in \(E^ n\), \(n\geq 5\). It is also shown that two two-surfaces in \(E^ n\) with the same \(\Gamma^ 2\) may differ only by either a homothetic transformation or a parallel translation.