Lorentz hypersurfaces in \(\mathbb{E}_1^{n + 1}\) satisfying \({\Delta} \overrightarrow{H} = \lambda \overrightarrow{H}\) with at most three distinct principal curvatures

DOI10.1016/J.JMAA.2015.09.017zbMath1331.53024OpenAlexW2661815250MaRDI QIDQ890499

Jiancheng Liu, Chao Yang

Publication date: 10 November 2015

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.2015.09.017

zbMATH Keywords

constant mean curvatureshape operatorpseudo-Euclidean spaceproper mean curvature vector fieldLorentz hypersurface

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Local submanifolds (53B25) Non-Euclidean differential geometry (53A35)

Related Items (5)

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

• Unnamed Item
• Isometric immersions of Lorentz space with parallel second fundamental forms
• 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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