A characterization of the Clifford torus

Abstract

In this paper, we prove that an n n -dimensional closed minimal hypersurface M M with Ricci curvature R i c ( M ) ≥ n 2 Ric(M) \geq \dfrac {n}{2} of a unit sphere S n + 1 ( 1 ) S^{n+1}(1) is isometric to a Clifford torus if n ≤ S ≤ n + 14 ( n + 4 ) 9 n + 30 n\leq S\leq n+\frac {14(n+4)}{9n+30} , where S S is the squared norm of the second fundamental form of M M .