On conformally flat submanifolds (Q1922783)

An immersed submanifold \(f: M^n\to\mathbb{R}^{n+p}\) in a standard flat Euclidean space, endowed with the induced metric, is said to be conformally flat if each point has a neighbourhood conformal to \(\mathbb{R}^n\). Around 1919, nonflat conformally flat hypersurfaces (\(p=1\), \(n\geq 4\)) were completely described by E. Cartan as being any envelope of a 1-parameter family of spheres. The authors generate Cartan's and Moore's results for \(p\leq n-3\). The remaining part of the paper is devoted to the local classification of all conformally flat submanifolds in codimension \(p=2\).