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Characterizations of linear Weingarten spacelike hypersurfaces in Lorentz space forms. (English) Zbl 1314.53104

Summary: In this article, we deal with complete linear Weingarten space-like hypersurfaces (that is, complete space-like 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 appropriate 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 space-like hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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