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Spheres in an Euclidean Space

Let M be an n-dimensional orientable compact hypersurface in an (n + 1)-dimensional Euclidean space R n+1 , n ≥ 2. If the gradient ∇α of the mean curvature α and the scalar curvature S of the hypersurface M satisfy the inequality Sk0 ≤ n(n − 1)k0α 2 − (n − 1) �∇ α� 2 where k0 is the infimum of the sectional curvatures of the hypersurface, then it is shown that α is a constant and M is the sphere in S n (α).