Sharp bounds for the norm of the traceless second fundamental form of complete linear Weingarten spacelike hypersurfaces

Abstract

We establish sharp bounds for the norm of the traceless second fundamental form of complete linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form and satisfying a suitable Okumura type inequality. As a consequence of these estimates, we derive new characterization results concerning totally umbilical spacelike hypersurfaces and hyperbolic cylinders of Lorentzian space forms.