Algebraic zero mean curvature varieties in semi-riemannian manifolds

Details Algebraic zero mean curvature varieties in semi-riemannian manifolds Algebraic zero mean curvature varieties in semi-riemannian manifolds

2009-03-13

arxiv.org/abs/0903.2387v1

Mathematics

Differential Geometry

16 pages

Scientific paper

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 in the de Sitter space.

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