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 ρ2 = S−nH2 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 ρ2 , K , Q and H and obtain some characterization theorems. Mathematics subject classification (2010): 53C42, 53C40.