LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE

CÍCERO P. AQUINO, HENRIQUE F. DE LIMA, MARCO ANTONIO L. VELÁSQUEZ
2014 Glasgow Mathematical Journal  
AbstractWe apply appropriate maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces with bounded mean curvature in the hyperbolic space. By supposing a suitable restriction on the norm of the traceless part of the second fundamental form, we show that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder, when its scalar curvature is positive, or to a spherical cylinder, when its scalar curvature is
more » ... negative. Related to the compact case, we also establish a rigidity result.
doi:10.1017/s0017089514000548 fatcat:wijhzilelveuxlhvrrmntuc3x4