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Lagrangian submanifolds attaining equality in the improved Chen's inequality

In [7] Oprea gave an improved version of Chen’s inequality for Lagrangian submanifolds of CP n (4). For minimal submanifolds this inequality coincides with a previous version proved in [5]. We consider here those non minimal 3-dimensional Lagrangian submanifolds in CP 3 (4) attaining at all points equality in the improved Chen inequality. We show how all such submanifolds may be obtained starting from a minimal Lagrangian surface in CP 2 (4).