Hypersurfaces of non-negative Ricci curvature in a Euclidean space (Q1201917)

Let \(M\) be a compact and connected hypersurface in a Euclidean space \(\mathbb{R}^{n+1}\) with the position vector field \(x\). It is proved that if the Ricci curvature of \(M\) is non-negative and the scalar curvature \(S\) of \(M\) satisfies \(\| x\|^ 2 S\leq n(n-1)\), then \(M\) is an imbedded sphere.