‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

Abstract

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎characterizations of the Riemannian products‎: ‎$S^{n-1}(a) times‎ ‎H^{1}(sqrt{a^2-1})$‎, ‎or $H^{n-1}(a) times H^1(sqrt{1-a^2})$‎.