Abstract
In this paper we provide a family of algebraic space-like surfaces in the three dimensional anti de Sitter space that shows that this Lorentzian manifold admits algebraic maximal examples 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.
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Perdomo, O.M. Algebraic zero mean curvature hypersurfaces in de Sitter and anti de Sitter spaces. Geom Dedicata 152, 183–196 (2011). https://doi.org/10.1007/s10711-010-9552-1
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DOI: https://doi.org/10.1007/s10711-010-9552-1