On space-like hypersurfaces in the de Sitter space (Q1907144)

The author investigates compact spacelike hypersurfaces in \(S^{n+1}_1\), where \(S^{n+1}_1\) is the (\(n+1\))-dimensional Lorentzian space form of positive constant curvature \(c\), often called de Sitter space. The author proves the following Theorem: Let \(M^n\) be an \(n\)-dimensional compact spacelike hypersurface in \(S^{n+1}_1\) with constant scalar curvature. If \(M^n\) satisfies \[ K(M)\geq 0,\quad R<c, \] where \(R\) is the normalized scalar curvature of \(M^n\), then \(M^n\) is isometric to a sphere. This improves a previous result of the author on such hypersurfaces.