Algebraic zero mean curvature varieties in semi-riemannian manifolds

2009/03/13 by Oscar Perdomo, Óscar Perdomo, Perdomo, Oscar
Mathematics · #53C42 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C42 #msc:53C50

paper · pdf · doi:10.48550/arxiv.0903.2387

16 pages

arxiv created 2009/03/13 · openalex publication_date 2009/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 in the de Sitter space.

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