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Algebraic zero mean curvature hypersurfaces in de Sitter and anti de Sitter spaces. (English) Zbl 1257.53091

Summary: In this paper we provide a family of algebraic space-like surfaces in the three dimensional anti de Sitter space showing that this Lorentzian manifold admits algebraic maximal hypersurfaces of any order. Then, we classify all the space-like order two algebraic maximal hypersurfaces in the anti de Sitter \(N\)-dimensional space. Finally, we provide two families of examples of Lorentzian order two algebraic zero mean curvature hypersurfaces in the de Sitter space.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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References:

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