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

DOI10.1007/s00605-015-0842-4zbMath1351.53064OpenAlexW2258283654MaRDI QIDQ328598

Keomkyo Seo, Sung-Hong Min

Publication date: 20 October 2016

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

Full work available at URL: https://doi.org/10.1007/s00605-015-0842-4

zbMATH Keywords

Ricci curvaturehigher-order mean curvatureClifford hypersurfaceSimons' integral inequality

Mathematics Subject Classification ID

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

Related Items (4)

Rigidity of hypersurfaces with constant higher order mean curvature in space forms ⋮ Characterizing small spheres in a unit sphere by Fischer-Marsden equation ⋮ Uniqueness of the catenoid and the Delaunay surface via a one-parameter family of touching spheres ⋮ Characterizations of a Clifford Hypersurface in a Unit Sphere

Cites Work

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• On hypersurfaces with two distinct principal curvatures in a unit sphere
• Complete hypersurfaces with constant mean curvature in a unit sphere
• Rigidity theorem for hypersurfaces in a unit sphere
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• Rigidity of minimal hypersurfaces of spheres with two principal curvatures
• Complete hypersurfaces with \(H_k=0\) in a unit sphere
• J. Simons' type integral formula for hypersurfaces in a unit sphere
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• Complete minimal surfaces in a sphere
• HYPERSURFACES IN A UNIT SPHERE Sⁿ⁺¹(1) WITH CONSTANT SCALAR CURVATURE
• A characterization of the Clifford torus
• Hypersurfaces with Constant Mean Curvature in Spheres
• A Characterization of Clifford Minimal Hypersurfaces in S 4
• 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
• Ricci curvature and minimal submanifolds.

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