Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures
type: Item
instance of: scholarly article
title: Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures
zbMATH Open document ID: 1203.53005
published in: Annals of Global Analysis and Geometry
publication date: 2010-10-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 5796344
zbMATH Keywords: Gauss curvature
zbMATH Keywords: normal curvature
zbMATH Keywords: squared mean curvature
zbMATH Keywords: Wintgen ideal surface
zbMATH Keywords: superminimal surface
zbMATH Keywords: Whitney sphere
author: Bang-Yen Chen
reviewed by: Mirjana Djoric
MaRDI profile type: Publication
full work available at URL: s10455-010-9205-5
OpenAlex ID: W2071501314
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DOI: 10.1007/S10455-010-9205-5
description: scientific article; zbMATH DE number 5796344