ON BI-HARMONIC HYPERSURFACES IN EUCLIDEAN SPACE OF ARBITRARY DIMENSION

DOI10.1017/S0017089514000524zbMath1323.53065MaRDI QIDQ2942600

Ram Shankar Gupta

Publication date: 11 September 2015

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

distinct principal curvaturesChen's bi-harmonic conjecture

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (11)

Unnamed Item ⋮ Lorentz hypersurfaces satisfying \(\triangle \vec {H}= \alpha \vec {H}\) with non diagonal shape operator ⋮ Hypersurfaces satisfying \(\triangle \overrightarrow{H} = \lambda \overrightarrow{H}\) in \(\mathbb{E}_s^5\) ⋮ Biharmonic \(\delta (r)\)-ideal hypersurfaces in Euclidean spaces are minimal ⋮ Biharmonic hypersurfaces in 5-dimensional non-flat space forms ⋮ Lorentz hypersurfaces in pseudo-Euclidean space \(E_1^5\) ⋮ Biharmonic hypersurfaces in Euclidean space \(E^{5}\) ⋮ Hypersurfaces in pseudo-Euclidean space with condition \(\Delta\mathbf{H}=\lambda\mathbf{H}\) ⋮ Biconservative hypersurfaces in Euclidean 5-space ⋮ On biharmonic hypersurfaces in 6-dimensional space forms ⋮ Biconservative hypersurfaces in space forms \(\overline{M}^{n+1}(c)\)

Cites Work

• Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean 5-space
• Biharmonic ideal hypersurfaces in Euclidean spaces
• Hypersurfaces of E4 with Harmonic Mean Curvature Vector
• Hypersurfaces in E⁴ with Harmonic Mean Curvature Vector Field

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