Closed hypersurfaces of \(S^4\) with two constant symmetric curvatures

DOI10.5802/afst.860zbMath0905.53041OpenAlexW2327074874MaRDI QIDQ1383397

Sebastião Carneiro de Almeida, Fabiano Gustavo Braga Brito

Publication date: 18 January 1999

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1997_6_6_2_187_0

zbMATH Keywords

constant curvatureisoparametric hypersurfaces of the 4-sphere

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (3)

Unnamed Item ⋮ Closed hypersurfaces of \(\mathbb S^4(1)\) with constant mean curvature and zero Gauß-Kronecker curvature ⋮ Total curvature of complete submanifolds of Euclidean space

Cites Work

• Unnamed Item
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• Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature
• Minimal cones and the spherical Bernstein problem. I
• 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
• The scalar curvature of minimal hypersurfaces in spheres
• Closed 3-dimensional hypersurfaces with constant mean curvature and constant scalar curvature
• Ruled Submanifolds of Space Forms with Mean Curvature of Nonzero Constant Length
• Hypersurfaces with Constant Mean Curvature in Spheres
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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