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

## TL;DR

This paper classifies all totally geodesic and homogeneous Lagrangian submanifolds within the nearly Kähler full flag manifold of -dimensional complex space, using Cartan's framework for differential invariants.

## Contribution

It provides a complete classification of certain Lagrangian submanifolds in a specific nearly Kähler manifold, applying Cartan's method to a new geometric setting.

## Key findings

- Classification of all totally geodesic Lagrangian submanifolds
- Classification of all homogeneous Lagrangian submanifolds
- Application of Cartan's framework to nearly Kähler geometry

## 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 $\mathbb{C}^3$.