On some cohomological properties of almost complex manifolds

2008/11/28 by Anna Fino, Fino, Anna, Адриано Томассини +1
Mathematics · #32C10 #53C25 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0811.4765

openalex publication_date 2008/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a special type of almost complex structures, called pure and full and introduced by T.J. Li and W. Zhang, in relation to symplectic structures and Hard Lefschetz condition. We provide sufficient conditions to the existence of the above type of almost complex structures on compact quotients of Lie groups by discrete subgroups. We obtain families of pure and full almost complex structures on compact nilmanifolds and solvmanifolds. Some of these families are parametrized by real 2-forms which are anti-invariant with respect to the almost complex structures.

Citations

• On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds

Related

• On non-pure forms on almost complex manifolds
• Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds
• On the Anti-Invariant Cohomology of Almost Complex Manifolds
• Invariant almost complex structures on real flag manifolds
• Almost abelian complex nilmanifolds