Hypersurfaces satisfying \(L_rx = Rx\) in sphere \(\mathbb S^{n+1}\) or hyperbolic space \(\mathbb H^{n+1}\)

DOI10.1007/S12044-009-0043-YzbMath1178.53055OpenAlexW2068227755WikidataQ126071633 ScholiaQ126071633MaRDI QIDQ1043864

Biao-Gui Yang, Xi-Min Liu

Publication date: 9 December 2009

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-009-0043-y

zbMATH Keywords

method of moving frames\(r\)-minimalisoparametric hypersurfacelinearized operator \(L_r\)

Mathematics Subject Classification ID

Global submanifolds (53C40)

Related Items (1)

\(r\)-minimal hypersurfaces in space forms

Cites Work

• Unnamed Item
• An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures
• Submanifolds in pseudo-Euclidean spaces satisfying the condition \({\Delta}x=Ax+B\)
• Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying \(\Delta x = Ax + B\)
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• On spacelike hypersurfaces of constant sectional curvature Lorentz manifolds
• Local rigidity theorems for minimal hypersurfaces
• Homogeneity and some curvature conditions for hypersurfaces
• Hypersurfaces in Space Forms Satisfying the Condition Δx = Ax + B

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