Pinching theorems of hypersurfaces in a unit sphere

DOI10.1016/J.DIFGEO.2011.09.001zbMath1228.53076OpenAlexW2035502229WikidataQ115356777 ScholiaQ115356777MaRDI QIDQ645473

Yun-tao Zhang

Publication date: 15 November 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2011.09.001

zbMATH Keywords

Ricci curvaturerigidityfundamental groupprinciple curvature

Mathematics Subject Classification ID

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

Related Items (1)

Characterizations of a Clifford hypersurface in a unit sphere via Simons' integral inequalities

Cites Work

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• Rigidity theorems of Clifford torus
• Complete hypersurfaces with constant mean curvature in a unit sphere
• Proof of the soul conjecture of Cheeger and Gromoll
• Chern's conjecture on minimal hypersurfaces
• Hypersurfaces of the Euclidean sphere with nonnegative Ricci curvature
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Complete minimal surfaces in a sphere
• The pinching constant of minimal hypersurfaces in the unit spheres
• Hypersurfaces with Constant Mean Curvature in Spheres
• A Characterization of Clifford Minimal Hypersurfaces in S 4
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• A pinching theorem for mimimal hypersurfaces in a sphere

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