On spacelike hypersurfaces with constant scalar curvature in the de Sitter space

On complete spacelike hypersurfaces with two distinct principal curvatures in Lorentz–Minkowski space

“…As for the case when the multiplicity of one of the two principal curvatures is n − 1, it corresponds to an ordinary differential equation. Otsuki's method can be generalized to study hypersurfaces in Riemannian space forms or spacelike hypersurfaces in Lorentzian space forms of constant mth mean curvature and two distinct principal curvatures (see e.g., [2][3][4][5][6][7]). …”

On spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces

“…An interesting result of Cheng and Ishikawa [6] states that the totally umbilical round spheres are the only compact spacelike hypersurfaces in S n+1 1 (1) with constant normalized scalar curvature R < 1. Some other authors, such as Brasil, Colares and Palmas [3], Camargo, Chaves and Sousa Jr. [4], Caminha [5], Hu, Scherfner and Zhai [10] and Li [11] have also worked on related problems.…”

On spacelike submanifolds with parallel mean curvature in an indefinite space form

“…In [3], Brasil et al obtained a gap theorem for hypersurfaces with constant scalar curvature in the de Sitter space. Recently, Hu et al [9] classified spacelike hypersurfaces M n in S n+1 1 (c) with constant scalar curvature and with two principal curvatures.…”