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

Abstract

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