Isometric immersions with homothetical Gauss map
The author classifies the isometric immersions f: \(M\to {\mathbb{R}}^ n\) from a simply connected, totally complete Riemannian manifold (M,g) into \({\mathbb{R}}^ n\) with flat normal bundle, a) for which the third fundamental form is a constant multiple of the Riemannian metric g, and b) whose third fundamental form is parallel. If f belongs to the class b), then it is a product of immersions of the class a); and if f belongs to the class a), then it is a product of standard embeddings of spheres and of special curves. The results follow from a careful investigation of the principal curvature distributions.
scientific article; zbMATH DE number 4151290