Submanifolds in pseudo-Euclidean spaces satisfying the condition \({\Delta}x=Ax+B\)

DOI10.1007/BF02414072zbMath0755.53012OpenAlexW2001648318MaRDI QIDQ1190976

Luis J. Alías, Pascual Lucas, Angel Ferrández

Publication date: 27 September 1992

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02414072

zbMATH Keywords

minimal hypersurfacetotally umbilical hypersurface

Mathematics Subject Classification ID

Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (8)

Orthogonal surfaces with constant mean curvature in the Euclidean 4- space ⋮ An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures ⋮ Hypersurfaces in pseudo-Euclidean spaces satisfying a linear condition on the linearized operator of a higher order mean curvature ⋮ Parabolic revolution surfaces of finite type in simply isotropic 3-spaces ⋮ Hypersurfaces in the Lorentz-Minkowski space satisfying \(L_{k} \psi = A\psi + b\) ⋮ Timelike hypersurfaces in the standard Lorentzian space forms satisfying \({L_kx=ax+b}\) ⋮ Invariant surfaces with coordinate finite-type Gauss map in simply isotropic space ⋮ Hypersurfaces satisfying \(L_rx = Rx\) in sphere \(\mathbb S^{n+1}\) or hyperbolic space \(\mathbb H^{n+1}\)

Cites Work

• An extension of Takahashi's theorem
• On surfaces of finite type in Euclidean 3-space
• Submanifolds of restricted type
• Minimal immersions of Riemannian manifolds
• Local rigidity theorems for minimal hypersurfaces
• Homogeneity and some curvature conditions for hypersurfaces
• Coordinate finite-type submanifolds
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