Complete hypersurfaces with constant mean curvature in a unit sphere

DOI10.1007/s00605-005-0377-1zbMath1129.53042OpenAlexW2052307413MaRDI QIDQ857849

Guoxin Wei

Publication date: 5 January 2007

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-005-0377-1

zbMATH Keywords

hypersurfacemean curvatureprincipal curvatures

Mathematics Subject Classification ID

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

Related Items (18)

Rotational surfaces in \(S^3\) with constant mean curvature ⋮ Nonnegative sectional curvature hypersurfaces in a real space form ⋮ Characterizations of a Clifford hypersurface in a unit sphere via Simons' integral inequalities ⋮ A new characterization of hyperbolic cylinder in anti-de Sitter space \(H_{1}^{n+1} (-1)\) ⋮ On the principal curvatures of complete minimal hypersurfaces in space forms ⋮ Pinching theorems of hypersurfaces in a unit sphere ⋮ Hypersurfaces with two distinct principal curvatures in a real space form ⋮ An estimate for the scalar curvature of constant mean curvature hypersurfaces in space forms ⋮ Hypersurfaces with nonzero constant Gauss-Kronecker curvature in \(M^{n+1}(\pm1)\) ⋮ Complete hypersurfaces with \(H_k=0\) in a unit sphere ⋮ ON COMPLETE SPACELIKE HYPERSURFACES WITH CONSTANT m-TH MEAN CURVATURE IN AN ANTI-DE SITTER SPACE ⋮ On hypersurfaces of spheres with two principal curvatures ⋮ Hypersurfaces with two distinct para-Blaschke eigenvalues in \(S^{n+1}(1)\) ⋮ On complete spacelike hypersurfaces with two distinct principal curvatures in a de Sitter space ⋮ LINEAR WEINGARTEN HYPERSURFACES IN A REAL SPACE FORM ⋮ RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE ⋮ On hypersurfaces with two distinct principal curvatures in a unit sphere ⋮ Free boundary constant mean curvature surfaces in a strictly convex three-manifold

Cites Work

• Global rigidity theorems of hypersurfaces
• Hypersurfaces with constant scalar curvature
• Hypersurfaces of the Euclidean sphere with nonnegative Ricci curvature
• Local rigidity theorems for minimal hypersurfaces
• Complete minimal surfaces in a sphere
• Familles de surfaces isoparametriques dans les espaces à courbure constante
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
• Hypersurfaces with constant scalar curvature in space forms

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