$\mathcal{F}$-harmonic 3-forms and the Type IIA flow on 6-dimensional symplectic Lie algebras

In this paper, we investigate the problem of $\mathcal{F}$-harmonic forms and the long-time behavior of the Type IIA flow on certain nilpotent and solvable symplectic Lie algebras (and corresponding nilmanifolds and solvmanifolds). In particular, we demonstrate that the Type IIA flow in these cases are very useful to detect desired geometric structures including Lagrangian torus fibrations and harmonic almost complex structures.