F-harmonic 3-forms and the Type IIA flow on 6-dimensional symplectic Lie algebras

2025/04/24 by Fei Teng, Fei, Teng
Mathematics · #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2504.17870

openalex publication_date 2025/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the problem of 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.

Related

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• The pluriclosed flow on nilmanifolds and Tamed symplectic forms
• Convergence of Type IIA manifolds and application to the Type IIA flow
• The Geometry of Three-Forms on Symplectic Six-Manifolds
• Soliton almost Kähler structures on 6-dimensional nilmanifolds for the symplectic curvature flow