Contact properties of codimension 2 submanifolds with flat normal bundle (Q616597)

Summary: Given an immersed submanifold \(M^n\subset \mathbb{R}^{n+2}\), we characterize the vanishing of the normal curvature \(R_D\) at a point \(p \in M\) in terms of the behaviour of the asymptotic directions and the curvature locus at \(p\). We relate the affine properties of codimension 2 submanifolds with flat normal bundle with the conformal properties of hypersurfaces in Euclidean space. We also characterize the semiumbilical, hyperspherical and conformally flat submanifolds of codimension 2 in terms of their curvature loci.