Rocky Mountain Journal of Mathematics

Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms

Cícero P. Aquino, Henrique F. de Lima, and Marco Antonio L. Velásquez

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Abstract

In this article, we deal with complete linear Weingarten spacelike hypersurfaces (that is, complete spacelike hypersurfaces whose mean and scalar curvatures are linearly related) immersed in a Lorentz space form. By assuming that the mean curvature attains its maximum and supposing appropriated restrictions on the norm of the traceless part of the second fundamental form, we apply Hopf's strong maximum principle in order to prove that such a spacelike hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 1 (2015), 13-27.

Dates
First available in Project Euclid: 7 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1428412772

Digital Object Identifier
doi:10.1216/RMJ-2015-45-1-13

Mathematical Reviews number (MathSciNet)
MR3334203

Zentralblatt MATH identifier
1314.53104

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Lorentz space forms linear Winegarten spacelike hypersurfaces second fundamental form totally umbilical hypersurfaces hyperbolic cylinders

Citation

Aquino, Cícero P.; Lima, Henrique F. de; Velásquez, Marco Antonio L. Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms. Rocky Mountain J. Math. 45 (2015), no. 1, 13--27. doi:10.1216/RMJ-2015-45-1-13. https://projecteuclid.org/euclid.rmjm/1428412772


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