Minimal hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature
type: Item
instance of: scholarly article
title: Minimal hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature
zbMATH Open document ID: 0602.53040
DOI: 10.1007/BF01161603
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183677
review text: Closed minimal hypersurfaces \(M^ 3\) with constant Gauss-Kronecker curvature and nowhere vanishing second fundamental form in the unit sphere \(S^ 4\) are classified in this paper. Precisely let K be the Gauss-Kronecker curvature of \(M^ 3\) (product of the principal curvatures). If \(K\neq 0\) then the hypersurface M is a standard minimal 3- dimensional Clifford torus in \(S^ 4\). If \(K=0\) and there are no points in M where the second fundamental form vanishes then M is the tube of a certain minimal surface \(\Sigma ^ 2\) in \(S^ 4\).
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 3971673
zbMATH Keywords: minimal hypersurfaces
zbMATH Keywords: Gauss-Kronecker curvature
zbMATH Keywords: Clifford torus
author: Sebastião Carneiro de Almeida
author: Fabiano G. B. Brito
MaRDI profile type: Publication
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OpenAlex ID: W1964638096
description: scientific article; zbMATH DE number 3971673