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首页> 外文期刊>Annali Dell Universita di Ferrara, Sezione VII. Scienze Matematiche >Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space
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Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space

机译：Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space

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Abstract Our aim in this paper is to study the uniqueness of complete spacelike hypersurfaces immersed in the anti-de Sitter space H1n+1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{mathbb {H}}}_1^{n+1}$$end{document}, through the behavior of their higher order mean curvatures. This is done by applying a suitable maximum principle concerning smooth vector fields whose norm is Lebesgue integrable on a complete Riemannian manifold. We also infer the nullity of complete r-maximal spacelike hypersurfaces and, in particular, we establish a nonexistence result concerning complete 1-maximal spacelike hypersurfaces in H1n+1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${{mathbb {H}}}_1^{n+1}$$end{document}.

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