Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures
Wintgen ideal surfaces in \(\mathbb E^4\) with equal Gauss \(K\) and normal \(K^D\) curvatures, i.e., Wintgen ideal surfaces which satisfy \(|K|=|K^D|\) identically, are completely classified. A surface in \(\mathbb E^4\) is called Wintgen ideal if it satisfies the equality case of the inequality \(K+|K^D|\leq H^2\) [proved by \textit{P. Wintgen} in C. R. Acad. Sci., Paris, Sér. A 288, 993--995 (1979; Zbl 0421.53003)] identically, where \(H^2\) is the squared mean curvature. Wintgen ideal surfaces in \(\mathbb E^4\) are exactly superminimal surfaces.
scientific article; zbMATH DE number 5796344
scientific article