Let M be a closed n-dimensional Riemannian manifold immersed in a unit sphere Sn+p,p≥2 , with parallel normalized mean curvature vector. Denote by 5 the square of the length of the second fundamental form of M. It is proved that if S ≤min{2n/3, 2(n-1)1/2}, then M is a hypersurface of a (n +1)-dimensional totally geodesic submanifold Sn+1 of Sn+p. This improve a result of Mo Xiaohuan. |