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On the geometry of linear Weingarten spacelike hypersurfaces in the de Sitter space

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Bulletin of the Brazilian Mathematical Society, New Series Aims and scope Submit manuscript

To prof. Antonio Gervasio Colares on occasion of his 80th birthday.

Abstract

Our purpose is to study the geometry of linear Weingarten spacelike hypersurfaces immersed in the de Sitter space \(\mathbb{S}_1^{n + 1} \). In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of the hyperbolic cylinders of \(\mathbb{S}_1^{n + 1} \). In the compact case, we obtain a rigidity result concerning to a such hypersurface according to the length of its second fundamental form.

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Authors and Affiliations

  1. Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58429-970, Campina Grande, PB, Brazil

    Henrique F. de Lima & Marco A. L. Velásquez

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  1. Henrique F. de Lima
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  2. Marco A. L. Velásquez
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Correspondence to Henrique F. de Lima.

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de Lima, H.F., Velásquez, M.A.L. On the geometry of linear Weingarten spacelike hypersurfaces in the de Sitter space. Bull Braz Math Soc, New Series 44, 49–65 (2013). https://doi.org/10.1007/s00574-013-0003-0

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  • DOI: https://doi.org/10.1007/s00574-013-0003-0

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