Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature
type: Item
instance of: scholarly article
title: Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature
zbMATH Open document ID: 0694.53054
DOI: 10.1007/BF02571269
author: Jayakumar Ramanathan
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174201
review text: The structure of minimal hypersurfaces in the four-sphere with vanishing Gauss-Kronecker curvature is studied. A technique of de Almeida and Brito constructs such hypersurfaces from minimal surfaces in the four sphere satisfying a curvature condition. In this paper, their technique is extended to cover the case where the minimal surface may have branch points. A theorem that characterizes any minimal hypersurface of the four-sphere with vanishing Gauss-Kronecker curvature as coming from this construction is then established.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4136935
zbMATH Keywords: minimal hypersurfaces
zbMATH Keywords: Gauss-Kronecker curvature
zbMATH Keywords: branch points
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4136935