On hypersurfaces of spheres with two principal curvatures

DOI10.1007/s00025-011-0144-7zbMath1253.53062OpenAlexW2024053879MaRDI QIDQ1758359

Ézio de Araujo Costa, Aldir Brasil Junior

Publication date: 9 November 2012

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-011-0144-7

zbMATH Keywords

Ricci curvaturesectional curvatureprincipal curvatureshypersurfaces in spheres

Mathematics Subject Classification ID

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

Related Items (1)

Rigidity of hypersurfaces with constant higher order mean curvature in space forms

Cites Work

• Complete hypersurfaces with constant mean curvature in a unit sphere
• A characterization of the Cartan hypersurface in a sphere
• On compact Riemannian manifolds with harmonic curvature
• Möbius isoparametric hypersurfaces in \(S^{n+1}\) with two distinct principal curvatures
• A Ricci inequality for hypersurfaces in the sphere
• Complete minimal surfaces in a sphere
• Classification of Möbius Isoparametric Hypersurfaces in ⁴
• Codazzi Tensor Fields, Curvature and Pontryagin Forms
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
• Rigidity theorems for closed hypersurfaces in space forms

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