$\mathcal{F}$-harmonic 3-forms and the Type IIA flow on 6-dimensional symplectic Lie algebras
Differential Geometry
2025-04-28 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Rings and Algebras
Symplectic Geometry
Abstract
In this paper, we investigate the problem of -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.
Keywords
Cite
@article{arxiv.2504.17870,
title = {$\mathcal{F}$-harmonic 3-forms and the Type IIA flow on 6-dimensional symplectic Lie algebras},
author = {Teng Fei},
journal= {arXiv preprint arXiv:2504.17870},
year = {2025}
}
Comments
27 pages, comments welcome! arXiv admin note: text overlap with arXiv:2405.04827