Hypersurfaces in non-flat Lorentzian space forms satisfying \(L_k \psi = a\psi + b\)

DOI10.11650/twjm/1500406685zbMath1254.53100arXiv1012.2778OpenAlexW1838000942MaRDI QIDQ439212

Pascual Lucas, Hector Fabián Ramírez-Ospina

Publication date: 1 August 2012

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2778

zbMATH Keywords

Newton transformationlinearized operator \(L_k\)Takahashi theoremhigher order mean curvaturesk-maximal hypersurface

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (7)

Complete spacelike hypersurfaces in the anti-de Sitter space: rigidity, nonexistence and curvature estimates ⋮ On the umbilicity of generalized linear Weingarten spacelike hypersurfaces in a Lorentzian space form ⋮ Normalized null hypersurfaces in nonflat Lorentzian space forms satisfying Lrx = Ux + b ⋮ Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space ⋮ Invariant surfaces with pointwise 1-type Gauss map in \(Sol_3\) ⋮ \(L_1\)-\(2\)-type surfaces in 3-dimensional de Sitter and anti de Sitter spaces ⋮ Timelike hypersurfaces in the standard Lorentzian space forms satisfying \({L_kx=ax+b}\)

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