Complete linear Weingarten hypersurfaces immersed in the hyperbolic space

摘要

In this paper, we apply the Hopf's strong maximum principle in order to obtain a suitable characterization of the complete linear Weingarten hypersurfaces immersed in the hyperbolic space H~(n+1). Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of H~(n+1).