In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space , that is, complete hypersurfaces of whose mean curvature and normalized scalar curvature satisfy for some , . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of . Furthermore, a rigidity result...
We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.
Download Results (CSV)