Gap theorems for Lagrangian submanifolds in complex space forms.

In this paper, we investigate the gap phenomena for complete Lagrangian submanifolds satisfying ∇ ∗ T ≡ 0 in complex space forms N n (4 c) , where T = 1 n ∇ ∗ B and B is the Lagrangian trace-free second fundamental form. We prove that under some pointwise or integral curvature pinching condition, the submanifold is either totally geodesic or isometric to the Whitney sphere. [ABSTRACT FROM AUTHOR]