\(r\)-minimal hypersurfaces in space forms

DOI10.1016/J.GEOMPHYS.2009.02.006zbMath1184.53067OpenAlexW1967780295MaRDI QIDQ1021778

Biao-Gui Yang, Xi-Min Liu

Publication date: 9 June 2009

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2009.02.006

zbMATH Keywords

\(r\)-minimal hypersurfacehypersurface of space form

Mathematics Subject Classification ID

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

Related Items (4)

Quadric hypersurfaces of \(L_r\)-finite type ⋮ On some \(L_k\)-finite-type Euclidean hypersurfaces ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures
• Hypersurfaces satisfying \(L_rx = Rx\) in sphere \(\mathbb S^{n+1}\) or hyperbolic space \(\mathbb H^{n+1}\)
• Hypersurfaces with constant scalar curvature
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• \(r\)-minimal submanifolds in space forms
• Complete hypersurfaces with \(H_k=0\) in a unit sphere
• On spacelike hypersurfaces of constant sectional curvature Lorentz manifolds
• Hypersurfaces Satisfying the Equation Δx = Rx + b
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature

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