Rigidity theorems of Clifford torus

In this article, we prove that the Clifford torus is the only closed hypersurface in the unit sphere Sn+1 (1) with infinite fundamental group, which satisfy r2 ≥ (n – 1)/n, RicM ≤ C−(H), and S ≤ S+(H). Moreover, we give a characterization of Clifford torus with