Weakly convex biharmonic hypersurfaces in nonpositive curvature space forms are minimal

DOI10.1007/S00025-013-0328-4zbMath1305.53024arXiv1305.7198OpenAlexW2058495258MaRDI QIDQ480874

Yong Luo

Publication date: 12 December 2014

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.7198

zbMATH Keywords

harmonic mean curvature vector fieldnonpositively curved space formsrough Laplacianweakly convex hypersurfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Local submanifolds (53B25)

Related Items (11)

The maximal principle for properly immersed submanifolds and its applications ⋮ Some recent progress of biharmonic submanifolds ⋮ \(L_k\)-biharmonic hypersurfaces in space forms ⋮ Recent progress of biharmonic hypersurfaces in space forms ⋮ Theory and numerics for Chen's flow of curves ⋮ Biharmonic hypersurfaces with constant scalar curvature in space forms ⋮ Topics in differential geometry associated with position vector fields on Euclidean submanifolds ⋮ On biminimal submanifolds in nonpositively curved manifolds ⋮ On Chen's biharmonic conjecture for hypersurfaces in \(\mathbb{R}^5\) ⋮ Unnamed Item ⋮ Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition LkHk+1 = λHk+1

Cites Work

• Biharmonic hypersurfaces in Riemannian manifolds
• On the generalized Chen's conjecture on biharmonic submanifolds
• Biharmonic submanifolds in a Riemannian manifold with non-positive curvature
• Biharmonic properly immersed submanifolds in Euclidean spaces
• Biharmonic maps into a Riemannian manifold of non-positive curvature
• Hypersurfaces of E4 with Harmonic Mean Curvature Vector
• BIHARMONIC PSEUDO-RIEMANNIAN SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACES
• BIHARMONIC SUBMANIFOLDS OF ${\mathbb S}^3$
• Hypersurfaces in E⁴ with Harmonic Mean Curvature Vector Field
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