Codimension two isometric immersions between Euclidean spaces (Q1064554)

Let \(E^ n\) be the flat Euclidean n-space with \(C^{\infty}\)- differentiability everywhere. \textit{P. Hartman} showed that any isometric immersion \(f: E^ n\to E^{n+2}\), \(n>1\), may be decomposed as a Riemannian product \(f=g\times id: E^ 2\times E^{n-2}\to E^ 4\times E^{n-2}\) [Trans. Am. Math. Soc. 147, 529-540 (1970; Zbl 0194.227)]. The present author uses this result to prove the following theorem: Let \(f: E^ n\to E^{n+2}\), \(n>1\), be an isometric immersion with nowhere zero normal curvature. Then f factors as the composition of isometric immersions, \(f=f_ 1\circ f_ 2: E^ n\to E^{n+1}\to E^{n+2}\). In order to show that the nonvanishing normal curvature is essential, counterexamples in the case of \(n=2\) are given.