Abstract
For an orientable compact and connected hypersurface in the Euclidean space Rn+1 with scalar curvature S, mean curvature a and sectional curvatures bounded below by a constant delta > 0, it is shown that the inequality
S <= n(n - 1)alpha(2) - (n - 1)delta(-1) parallel to del alpha parallel to(2)
implies that the hypersurface is a sphere, where del alpha is the gradient of alpha.