New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space
Cícero P. Aquino, Henrique F. de Lima (2015)
Archivum Mathematicum
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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,...