Space-like submanifolds with constant scalar curvature
The main result of this paper is the following: Let \(M^n\) be an \(n\)-dimensional compact space-like submanifold with constant scalar curvature and nonnegative sectional curvature immersed in a de Sitter space \(M_p^{n+p}(c).\) If \(M^n\) has flat normal bundle and the normalized scalar curvature \(R\) of \(M^n\) satisfies \(R<c,\) then \(M^n\) is totally umbilical and isometric to a sphere.
scientific article; zbMATH DE number 1643171