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It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken,Curvature inequalities for Lagrangian submanifolds: the final solution, Differ.Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold $M$ of acomplex space form $\tilde M^{n}(4c)$ of constant holomorphic sectionalcurvature $4c$ satisfies the following optimal inequality: \begin{align*}\delta(2,n-2) \leq \frac{n^2(n-2)}{4(n-1)} H^2 + 2(n-2) c, \end{align*} where$H^2$ is the squared mean curvature and $\delta(2,n-2)$ is a $\delta$-invarianton $M$. In this paper we classify Lagrangian submanifolds of complex spaceforms $\tilde M^{n}(4c)$, $n \geq 5$, which satisfy the equality case of thisinequality at every point.

Classification of $\delta(2,n-2)$-ideal Lagrangian submanifolds in $n$-dimensional complex space forms