WILLMORE LAGRANGIAN SUBMANIFOLDS IN COMPLEX PROJECTIVE SPACE

Let M be an n-dimensional compact Willmore Lagrangian submanifold in a complex projective space CPn and let S and H be the squared norm of the second fundamental form and the mean curvature of M. Denote by rho(2) = S-nH(2) the non-negative function on M, K and Q the functions which assign to each point of M the infimum of the sectional curvature and Ricci curvature at the point. We prove some integral inequalities of Simons' type for n-dimensional compact Willmore Lagrangian submanifolds in CPn in terms of rho(2), K, Q and H and obtain some characterization theorems.