Rigidity theorem for hypersurfaces in a unit sphere

DOI10.1007/s00605-005-0378-0zbMath1110.53050OpenAlexW2024159673MaRDI QIDQ863491

Guoxin Wei

Publication date: 26 January 2007

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

Full work available at URL: https://doi.org/10.1007/s00605-005-0378-0

zbMATH Keywords

torussubmanifoldprincipal curvaturesClifford minimal hypersurfaceGauss equations

Mathematics Subject Classification ID

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

Related Items

Characterizations of a Clifford hypersurface in a unit sphere via Simons' integral inequalities ⋮ Rigidity of hypersurfaces with constant higher order mean curvature in space forms ⋮ On the principal curvatures of complete minimal hypersurfaces in space forms ⋮ Characterizations of a Clifford Hypersurface in a Unit Sphere ⋮ J. Simons' type integral formula for hypersurfaces in a unit sphere ⋮ RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE ⋮ EMBEDDED HYPERSURFACES WITH CONSTANT mTH MEAN CURVATURE IN A UNIT SPHERE ⋮ Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space H 1 n+1 (−1)

Cites Work

• Global rigidity theorems of hypersurfaces
• Hypersurfaces with constant scalar curvature
• Rigidity of Clifford minimal hypersurfaces
• Rigidity of minimal hypersurfaces of spheres with two principal curvatures
• Local rigidity theorems for minimal hypersurfaces
• Familles de surfaces isoparametriques dans les espaces à courbure constante
• Submanifolds with Constant Mean Curvature
• Submanifolds with Constant Mean Curvature II
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• Hypersurfaces with constant scalar curvature in space forms
• A pinching theorem for mimimal hypersurfaces in a sphere