Compositions of isometric immersions in higher codimension
Luis A. Florit | Dajczer, Marcos
Given an n-dimensional Euclidean submanifold M in codimension p <= 6, we show, under generic conditions on its second fundamental form, that any other isometric immersion of M into Euclidean space in codimension p+q, 0 <= q <= n-2p-1 and 2q <= n+1 if q >= 5, must be locally a composition of isometric immersions. This generalizes several previous results on rigidity and compositions of submanifolds. We also provide conditions under which our result is global.