For an orientable compact and connected positively curved hypersurface in the Euclidean space Rn+1, n > 2, with scalar curvature S, shape operator A and mean curvature alpha, it is shown that the inequality parallel toAparallel to(2) S greater than or equal to (1)/(2) parallel toRparallel to(2) + parallel toQparallel to(2) + 2n(n-1)parallel todelalphaparallel to(2) implies that the hypersurface is a sphere, where delalpha is the gradient of alpha, and parallel toRparallel to, parallel toQparallel to are the lengths of the curvature tensor field R, the Ricci operator Q of the hypersurface respectively.
