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In this article the framework created by Cartan to produce local differentialinvariants for submanifolds of homogeneous spaces is applied to classify alltotally geodesic Lagrangian submanifolds and all homogeneous Lagrangiansubmanifolds of the nearly K\"ahler manifold of full flags in $\mathbb{C}^3$.

Lagrangian submanifolds of the nearly K\"ahler full flag manifold $F_{1,2}(\mathbb{C}^3)$