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 scalar curvature in a unit sphere, they classified the submanifold. Let M be a hypersurface with vanishing Moebius form and harmonic curvature in a unit sphere, we discuss some properties of the hypersurface; let M be a compact sub-manifold with vanishing Moebius form and a sectional curvature satisfied a certain condition, we discuss some properties of the submanifold in this paper.