Rocky Mountain Journal of Mathematics
- Rocky Mountain J. Math.
- Volume 45, Number 1 (2015), 13-27.
Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms
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.
Rocky Mountain J. Math., Volume 45, Number 1 (2015), 13-27.
First available in Project Euclid: 7 April 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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