On complete spacelike hypersurfaces with two distinct principal curvatures in a de Sitter space

We investigate complete spacelike hypersurfaces in a de Sitter space with two distinct principal curvatures and constant m  -th mean curvature. By using Otsukiʼs idea, we obtain some global classification results. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in de Sitter (n+1)(n+1)-spaces S1n+1(1) (n⩾3n⩾3) of constant m  -th mean curvature Hm(|Hm|⩾1)Hm(|Hm|⩾1) with two distinct principal curvatures λ and μ   satisfying inf(λ−μ)2>0 are the hyperbolic cylinders. We also obtain some global rigidity results for hyperbolic cylinders and obtain some non-existence results.