Isometric deformations of compact Euclidean submanifolds in codimension 2 (Q1913353)

Let \(M^n\) be a compact Riemannian manifold, immersed in \(\mathbb{R}^{n+2}\). The authors prove that any isometric deformation of the immersion is almost everywhere induced by isometric deformation of hypersurfaces. As a consequence, a rigidity theorem for codimension 2 Euclidean submanifolds is derived in terms of intrinsic curvature conditions.