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2015 Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms
Cícero P. Aquino, Henrique F. de Lima, Marco Antonio L. Velásquez
Rocky Mountain J. Math. 45(1): 13-27 (2015). DOI: 10.1216/RMJ-2015-45-1-13


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.


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Cícero P. Aquino. Henrique F. de Lima. Marco Antonio L. Velásquez. "Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms." Rocky Mountain J. Math. 45 (1) 13 - 27, 2015.


Published: 2015
First available in Project Euclid: 7 April 2015

zbMATH: 1314.53104
MathSciNet: MR3334203
Digital Object Identifier: 10.1216/RMJ-2015-45-1-13

Primary: 53C42
Secondary: 53A10 , 53C20 , 53C50

Keywords: hyperbolic cylinders , linear Winegarten spacelike hypersurfaces , Lorentz space forms , second fundamental form , Totally umbilical hypersurfaces

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium


Vol.45 • No. 1 • 2015
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