Complete CMC hypersurfaces in the hyperbolic space with prescribed Gauss mapping
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- by Abdênago Barros, Cícero Aquino and Henrique de Lima PDF
- Proc. Amer. Math. Soc. 142 (2014), 3597-3604 Request permission
Abstract:
Our aim in this paper is to show that a complete hypersurface $x:M^{n}\to \mathbb {H}^{n+1}$ immersed with constant mean curvature into the hyperbolic space $\mathbb {H}^{n+1}$ is totally umbilical provided that its Gauss mapping $\nu$ has some suitable behavior. In this setting, our first result requires that the image $\nu (M)$ lies in a totally umbilical spacelike hypersurface of the de Sitter space $\mathbb S_1^{n+1}$, while in our second one we suppose that $M^n$ has scalar curvature bounded from below and that $\nu (M)$ is contained in the closure of a domain enclosed by a totally umbilical spacelike hypersurface of $\mathbb {S}_1^{n+1}$ determined by some vector $a$ of the Minkowski space $\mathbb {L}^{n+2}$, with the tangential component of $a$ with respect to $M^n$ having Lebesgue integrable norm.References
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Additional Information
- Abdênago Barros
- Affiliation: Departamento de Matemática, Universidade Federal do Ceará, 60455-760 Fortaleza, Ceará, Brazil
- Email: abbarros@mat.ufc.br
- Cícero Aquino
- Affiliation: Departamento de Matemática, Universidade Federal do Piauí, 64049-550 Teresina, Piauí, Brazil
- Email: cicero.aquino@ufpi.edu.br
- Henrique de Lima
- Affiliation: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil
- MR Author ID: 800981
- Email: henrique@dme.ufcg.edu.br
- Received by editor(s): August 6, 2012
- Received by editor(s) in revised form: October 10, 2012
- Published electronically: June 10, 2014
- Communicated by: Lei Ni
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 3597-3604
- MSC (2010): Primary 53C42; Secondary 53C50
- DOI: https://doi.org/10.1090/S0002-9939-2014-12118-6
- MathSciNet review: 3238435