Hypersurfaces in \(\mathbb{E}_s^{n + 1}\) satisfying \(\operatorname{\Delta} \overrightarrow{H} = \lambda \overrightarrow{H}\) with at most two distinct principal curvatures

DOI10.1016/J.JMAA.2017.01.090zbMath1360.53065OpenAlexW2584238749MaRDI QIDQ517934

Jiancheng Liu, Chao Yang

Publication date: 28 March 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.01.090

zbMATH Keywords

hypersurfacemean curvatureshape operatorisoparametricpseudo-euclidean space

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Non-Euclidean differential geometry (53A35) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (5)

A class of hypersurfaces in \(\mathbb{E}^{n+1}_s\) satisfying \(\Delta \vec{H} = \lambda\vec{H} \) ⋮ Classification of \(f\)-biharmonic submanifolds in Lorentz space forms ⋮ On some geometric properties of quasi-product production models ⋮ On \(\eta\)-biharmonic hypersurfaces with constant scalar curvature in higher dimensional pseudo-Riemannian space forms ⋮ On \(\eta\)-biharmonic hypersurfaces in pseudo-Riemannian space forms

Cites Work

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• Hypersurfaces of \(E_s^4\) with proper mean curvature vector
• Hypersurfaces of type \(M^3_2\) in \(E^4_2\) with proper mean curvature vector
• Hypersurfaces in \(\mathbb E_s^{n+1}\) satisfying \(\Delta\overrightarrow H=\lambda\overrightarrow H\) with at most three distinct principal curvatures
• Lorentzian isoparametric hypersurfaces
• Lorentz hypersurfaces in \(E_{1}^{4}\) satisfying \(\Delta\overset\rightarrow H=\alpha \overset\rightarrow H\)
• BIHARMONIC SURFACES IN PSEUDO-EUCLIDEAN SPACES

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