Submanifolds with Moebius Sectional Curvature in a Unit Sphere

Let M be a hypersurface with the parallal Moebius second curvature in a unit sphere. HU Zejun and LI Haizhong classified the hypersurface. Let M be a compact submanifold with constant scarlar curvature in a unit sphere, they classified the submanifold. Let M be a hypersurface with vanishing Moe- bius form and hramonic curvature in a unit sphere, we dicuss some properties of the hypersurface; let M be a compact sub- manifold with vanishing Moebius form and a sectional curva-ture satisfied a certain condition, we dicuss some properties of the submanifold in this paper.