Primitive decompositions of Dolbeault harmonic forms on compact almost-Kähler manifolds

2022/01/23 by Andrea Cattaneo, Cattaneo, Andrea, Nicoletta Tardini +3
Mathematics · #53C15 #58A14 #58J05 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.09273

openalex publication_date 2022/01/23 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let (X,J,g,ω) be a compact 2n-dimensional almost-Kähler manifold. We prove primitive decompositions of ∂-, ∂-harmonic forms on X in bidegree (1,1) and (n-1,n-1) (such bidegrees appear to be optimal). We provide examples showing that in bidegree (1,1) the ∂- and ∂-decompositions differ.

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