Submanifolds with parallel normalized mean curvature vector in a unit sphere

Let M ⁿ be an n-dimensional closed submanifold of a sphere with parallel normalized mean curvature vector. Denote by S and H the squared norm of the second fundamental form and the mean curvature of M ⁿ , respectively. Assume that the fundamental group ({pi_{1}(M^{n})}) of M ⁿ is infinite and ({S, leqslant, S(H)=n+frac{n^{3}H^{2}}{2(n-1)}-frac{n(n-2)H}{2(n-1)}sqrt{n^{2}H^{2}+4(n-1)}}), then S is constant, S = S(H), and M ⁿ is isometric to a Clifford torus ({S^{1}(sqrt{1-r^{2}})times S^{n-1}(r)}) with ({r^{2}leqslant frac{n-1}{n}}).