Classification of proper biharmonic hypersurfaces in pseudo-Riemannian space forms

DOI10.1016/j.difgeo.2015.05.001zbMath1322.53052OpenAlexW337657347WikidataQ115355924 ScholiaQ115355924MaRDI QIDQ2349437

Jiancheng Liu, Li Du

Publication date: 22 June 2015

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2015.05.001

zbMATH Keywords

shape operatoranti-de Sitter spaceprinciple curvatures

Mathematics Subject Classification ID

Global submanifolds (53C40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (11)

Biharmonic vector fields on pseudo-Riemannian manifolds ⋮ Hypersurfaces satisfying \(\tau_2(\phi)=\eta\tau (\phi)\) in pseudo-Riemannian space forms ⋮ Triharmonic hypersurfaces with constant mean curvature in pseudo-Riemannian space forms ⋮ Polyharmonic hypersurfaces into pseudo-Riemannian space forms ⋮ Biharmonic hypersurfaces in pseudo-Riemannian space forms with at most two distinct principal curvatures ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Biharmonic submanifolds of pseudo-Riemannian manifolds ⋮ Classification of \(\eta \)-biharmonic surfaces in non-flat Lorentz space forms ⋮ Biharmonic submanifolds with parallel normalized mean curvature vector field in pseudo-Riemannian space forms ⋮ On \(\eta\)-biharmonic hypersurfaces in pseudo-Riemannian space forms

Cites Work

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• 2-harmonic maps and their first and second variational formulas
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• QUASI-MINIMAL LAGRANGIAN SURFACES WHOSE MEAN CURVATURE VECTORS ARE EIGENVECTORS
• BIHARMONIC SUBMANIFOLDS OF ${\mathbb S}^3$

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