Codimension two isometric immersions between Euclidean spaces

Abstract

Hartman and Nirenberg showed that any C°° isometric immersion/: E" -> E"+1 between flat Euclidean spaces is a cylinder erected over a plane curve.We show that in the codimension two case, /: E" -» E" +2 factors as a composition of isometric immersions/ ~ f\° fe E" -» E" +1 -* E w+2 , when n > 1 and /has nowhere zero normal curvature.