Translation surfaces in the 3-dimensional space satisfying \(\Delta ^{III} r_{i} = \mu _{i} r_{i}\)

DOI10.1007/s00022-012-0136-0zbMath1262.53005OpenAlexW2132693316WikidataQ126092589 ScholiaQ126092589MaRDI QIDQ1945678

Mohammed Bekkar, Bendehiba Senoussi

Publication date: 8 April 2013

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-012-0136-0

zbMATH Keywords

minimal surfacesLaplacian operatortranslation surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Surfaces in Euclidean and related spaces (53A05) Non-Euclidean differential geometry (53A35)

Related Items (14)

Rotational hypersurfaces in Lorentz-Minkowski 4-space ⋮ Unnamed Item ⋮ THA-surfaces of finite type in the Galilean space \(\mathbb{G}^3\) ⋮ Unnamed Item ⋮ Classification of space-like translation surfaces in the 3-dimensional Lorentz Heisenberg group H3 ⋮ Translation surfaces of finite type in ${\rm Sol}_{3}$ ⋮ Translation surfaces in affine 3-space ⋮ Homothetical surfaces in three dimensional pseudo-Galilean spaces satisfying \(\Delta ^{II}\mathbf{x }_i=\lambda _i\mathbf{x }_i\) ⋮ Caustics of translation surfaces in Euclidean 3-space ⋮ Translation surfaces in the three-dimensional simply isotropic space 𝕀31 ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On curvatures and points of the translation surfaces in Euclidean 3-space ⋮ Unnamed Item

Cites Work

• Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying \(\Delta ^{II}r_{i} = \lambda _{i}r_{i}\)
• On surfaces of finite type in Euclidean 3-space
• Hypersurfaces of \(E_s^4\) with proper mean curvature vector
• Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying \(\Delta^{II}\vec r=A\vec r\)
• Surfaces of revolution satisfying $\triangle^{III}\boldsymbol{x}=A\boldsymbol{x}$
• Ruled surfaces whose mean curvature vector is an eigenvector of the Laplacian of the second fundamental forms
• Hypersurfaces in Space Forms Satisfying the Condition Δx = Ax + B
• Unnamed Item
• Unnamed Item

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