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

DOI10.1016/j.jmaa.2014.04.066zbMath1296.53126OpenAlexW2081564742MaRDI QIDQ2252488

Chao Yang, Jiancheng Liu

Publication date: 17 July 2014

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.2014.04.066

zbMATH Keywords

hypersurfaceshape operatorpseudo-Euclidean spacediagonalizableproper mean curvature vector field

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (12)

A class of hypersurfaces in \(\mathbb{E}^{n+1}_s\) satisfying \(\Delta \vec{H} = \lambda\vec{H} \) ⋮ Hypersurfaces satisfying \(\tau_2(\phi)=\eta\tau (\phi)\) in pseudo-Riemannian space forms ⋮ Lorentz hypersurfaces satisfying \(\triangle \vec {H}= \alpha \vec {H}\) with non diagonal shape operator ⋮ Lorentz hypersurfaces in \(\mathbb{E}_1^{n + 1}\) satisfying \({\Delta} \overrightarrow{H} = \lambda \overrightarrow{H}\) with at most three distinct principal curvatures ⋮ Hypersurfaces satisfying \(\triangle \overrightarrow{H} = \lambda \overrightarrow{H}\) in \(\mathbb{E}_s^5\) ⋮ Biharmonic hypersurfaces in pseudo-Riemannian space forms with at most two distinct principal curvatures ⋮ Lorentz hypersurfaces in pseudo-Euclidean space \(E_1^5\) ⋮ Hypersurfaces in \(\mathbb{E}_s^{n + 1}\) satisfying \(\operatorname{\Delta} \overrightarrow{H} = \lambda \overrightarrow{H}\) with at most two distinct principal curvatures ⋮ Hypersurfaces in pseudo-Euclidean space with condition \(\Delta\mathbf{H}=\lambda\mathbf{H}\) ⋮ On \(\eta\)-biharmonic hypersurfaces with constant scalar curvature in higher dimensional pseudo-Riemannian space forms ⋮ On \(\eta\)-biharmonic hypersurfaces in pseudo-Riemannian space forms ⋮ Classification of proper biharmonic hypersurfaces in pseudo-Riemannian space forms

Cites Work

• On surfaces in the 3-dimensional Lorentz-Minkowski space
• Hypersurfaces of \(E_s^4\) with proper mean curvature vector
• Null 2-type surfaces in \(E^ 3\) are circular cylinders
• Classifying hypersurfaces in the Lorentz-Minkowski space with a characteristic eigenvector
• A classification of certain 3-dimensional conformally flat Euclidean hypersurfaces
• Hypersurfaces of \(\bar\mathbb{E}^ 4\) satisfying \(\Delta\vec H=\lambda\vec H\)
• Hypersurfaces of type \(M^3_2\) in \(E^4_2\) with proper mean curvature vector
• Lorentz hypersurfaces in \(E_{1}^{4}\) satisfying \(\Delta\overset\rightarrow H=\alpha \overset\rightarrow H\)
• BIHARMONIC SURFACES IN PSEUDO-EUCLIDEAN SPACES
• BIHARMONIC PSEUDO-RIEMANNIAN SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACES
• Submanifolds with harmonic mean curvature vector field in contact 3-manifolds
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