Minimal hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature

DOI10.1007/BF01161603zbMath0602.53040OpenAlexW1964638096MaRDI QIDQ1081852

Sebastião Carneiro de Almeida, Fabiano Gustavo Braga Brito

Publication date: 1987

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/183677

zbMATH Keywords

Clifford torusGauss-Kronecker curvatureminimal hypersurfaces

Mathematics Subject Classification ID

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

Related Items (13)

Gap theorems for minimal submanifolds of a hyperbolic space ⋮ Unnamed Item ⋮ On deformable minimal hypersurfaces in space forms ⋮ Minimal hypersurfaces in $ {\mathbb{S}}^5$ with vanishing Gauss–Kronecker curvature ⋮ Closed hypersurfaces of \(S^4\) with two constant symmetric curvatures ⋮ The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms ⋮ Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature ⋮ Rigidity and stability estimates for minimal submanifolds in the hyperbolic space ⋮ Complete hypersurfaces in a 4-dimensional hyperbolic space ⋮ Closed hypersurfaces of \(\mathbb S^4(1)\) with constant mean curvature and zero Gauß-Kronecker curvature ⋮ Total curvature of complete submanifolds of Euclidean space ⋮ Complete minimal hypersurfaces in the hyperbolic space ℍ⁴ with vanishing Gauss-Kronecker curvature ⋮ Divergence-preserving geodesic transformations

Cites Work

• Unnamed Item
• Remarks on closed minimal submanifolds in the standard Riemannian m- sphere
• Local rigidity theorems for minimal hypersurfaces
• Familles de surfaces isoparametriques dans les espaces à courbure constante
• Minimal hypersurfaces of S4 with non zero Gauss-Kronecker curvature
• On Minimal Immersions of S 2 Into S 2m
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

This page was built for publication: Minimal hypersurfaces of \(S^ 4\) with constant Gauss-Kronecker curvature