Oscar Palmas

Complete rotation hypersurfaces with Hk constant in space forms

In this paper we classify all complete rotation hypersurfaces withHk constant in ℝn+1 andHn+1, is the normalizedk-th symmetric function of the principal curvatures. Partial results are also given forHn+1.

A gap theorem for complete constant scalar curvature hypersurfaces in the de Sitter space

To each immersed complete space-like hypersurfaceM with constant normalized scalar curvature R in the de Sitter space S nC1 1 , we associate sup H 2 , where H is the mean curvature of M .I t is proved that the condition sup H 2 Cn. N R/, where N R D .R 1 /> 0 and Cn. N R/ is a constant depending only on R and n, implies that either M is totally umbilical or M is a hyperbolic cylinder. It is also proved the sharpness of this result by showing the existence of a class of new rotation constant scalar curvature hypersurfaces in S nC1 1 such that sup H 2 >C n. N R/.