THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE

DOI10.1142/S021919970700237XzbMath1123.53031MaRDI QIDQ5297259

Hae Young Yang, Young Jin Suh

Publication date: 18 July 2007

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

second fundamental formscalar curvatureminimal hypersurface in a sphere

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (19)

The second pinching theorem for hypersurfaces with constant mean curvature in a sphere ⋮ An optimal gap theorem for scalar curvature of CMC hypersurfaces in a sphere ⋮ A new gap for complete hypersurfaces with constant mean curvature in space forms ⋮ A note on the Chern conjecture in dimension four ⋮ WARPED PRODUCTS IN RIEMANNIAN MANIFOLDS ⋮ On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers ⋮ Characterizing small spheres in a unit sphere by Fischer-Marsden equation ⋮ On the Chern conjecture for isoparametric hypersurfaces ⋮ Complete hypersurfaces with 𝑤-constant mean curvature in the unit spheres ⋮ A new pinching theorem for complete self-shrinkers and its generalization ⋮ A new characterization of the Clifford torus via scalar curvature pinching ⋮ On rigidity of Clifford torus in a unit sphere ⋮ A sufficient condition for a hypersurface to be isoparametric ⋮ On Chern's problem for rigidity of minimal hypersurfaces in the spheres ⋮ On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere ⋮ A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces ⋮ CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES ⋮ Global rigidity theorems for submanifolds with parallel mean curvature ⋮ Closed Willmore minimal hypersurfaces with constant scalar curvature in \(\mathbb{S}^5(1)\) are isoparametric

Cites Work

• Complete space-like hypersurfaces in locally symmetric Lorentz spaces
• An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere
• Chern's conjecture on minimal hypersurfaces
• The scalar curvature of minimal hypersurfaces in spheres
• The rigidity of Clifford torus \(S^ 1(\sqrt{\frac1n})\times S^{n-1}(\sqrt{\frac{n-1}n})\)
• Minimal varieties in Riemannian manifolds
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• A pinching theorem for mimimal hypersurfaces in a sphere

This page was built for publication: THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE