Affine umbilical surfaces in \(\mathbb{R}^ 4\)
Consider a surface with codimension 2 in \(\mathbb{R}^4\). There exist different approaches to a theory leading to different canonically determined transversal planes. Here the authors follow an approach of \textit{K. Nomizu} and \textit{L. Vrancken} [Int. J. Math. 4, No. 1, 127-165 (1993; Zbl 0810.53006)]. If for any vector field \(\xi\) in the associated transverse plane the induced Weingarten operator \(S\) is a multiple of the identity operator on the tangent plane, the surface is called affine umbilical. The authors give classifications of subclasses of this class of surfaces.
scientific article; zbMATH DE number 871768