Strictly nearly Kahler 6-manifolds are not compatible with symplectic forms

2006/10/26 by Mehdi Lejmi, Lejmi, Mehdi
Mathematics · #53B35 #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.math/0610806

openalex publication_date 2006/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the almost complex structure underlying a non-Kahler, nearly Kahler 6-manifold (in particular, the standard almost complex structure of S⁶) cannot be compatible with any symplectic form, even locally.

Related

• S⁶ and the geometry of nearly Kähler 6-manifolds
• About integrability of almost complex structures on strictly Nearly Kähler 6-manifolds
• Nearly Kähler submanifolds of a space form
• A 6-dimensional simply connected complex and symplectic manifold with no Kähler metric
• Families of almost complex structures and transverse (p,p)-forms