EMBEDDED HYPERSURFACES WITH CONSTANT mTH MEAN CURVATURE IN A UNIT SPHERE

DOI10.1142/S0219199710004081zbMath1213.53081arXiv0904.0299OpenAlexW2963880866MaRDI QIDQ3067171

Qing-Ming Cheng, Haizhong Li, Guoxin Wei

Publication date: 20 January 2011

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

Full work available at URL: https://arxiv.org/abs/0904.0299

zbMATH Keywords

unit sphereembedded hypersurfacesconstant \(m\)-th mean curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometric aspects of harmonic maps (53C43)

Related Items

Hypersurfaces with constant \(m\)th mean curvature in the spheres, A class of minimal Lagrangian submanifolds in complex hyperquadrics, A lower bound for areas of the rotational hypersurfaces with 𝐻ₘ=0 in the spheres

Cites Work

• Rigidity theorem for hypersurfaces in a unit sphere
• Rotational hypersurfaces of space forms with constant scalar curvature
• Embedded rotational hypersurfaces with constant scalar curvature in \(S^n\): a correction to a statement in M.~L.~Leite, Manuscripta Math. 67, 285--304 (1990; Zbl 695.53040).
• Compact embedded rotation hypersurfaces of \(S^{n+1}\)
• HYPERSURFACES IN A UNIT SPHERE Sⁿ⁺¹(1) WITH CONSTANT SCALAR CURVATURE
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature