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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 \({{\mathbb {H}}}_1^{n+1}\), 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 \({{\mathbb {H}}}_1^{n+1}\).

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Acknowledgements

The first author is partially supported by CAPES, Brazil. The second and third authors are partially supported by CNPq, Brazil, grants 301970/2019-0 and 311224/2018-0, respectively.

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  1. Departamento de Matemática, Universidade Federal de Campina Grande, Campina Grande, Paraíba, 58109-970, Brazil

    Weiller F. C. Barboza, Henrique F. de Lima & Marco Antonio L. Velásquez

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  1. Weiller F. C. Barboza
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  2. Henrique F. de Lima
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  3. Marco Antonio L. Velásquez
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Correspondence to Henrique F. de Lima.

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Barboza, W.F.C., de Lima, H.F. & Velásquez, M.A.L. Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space. Ann Univ Ferrara 69, 95–109 (2023). https://doi.org/10.1007/s11565-022-00403-y

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