Closed hypersurfaces of \(\mathbb S^4(1)\) with constant mean curvature and zero Gauß-Kronecker curvature

DOI10.1016/J.CRMA.2005.01.005zbMath1069.53049OpenAlexW1976476557MaRDI QIDQ1776840

André Gomes de Oliveira, Tsasa Lusala

Publication date: 12 May 2005

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2005.01.005

zbMATH Keywords

hypersurfaceminimal hypersurfacesGauß-Kronecker curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature
• Minimal hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature
• A closed hypersurface with constant scalar and mean curvatures in \(\mathbb{S}^ 4\) is isoparametric
• On closed hypersurfaces of constant scalar curvatures and mean curvatures in \(S^{n+1}\)
• Closed hypersurfaces of \(S^4\) with two constant symmetric curvatures
• The scalar curvature of minimal hypersurfaces in spheres

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