Primitive decompositions of Dolbeault harmonic forms on compact almost-K\"ahler manifolds

In complex geometry the Dolbeault cohomology plays a fundamental role in the study of complex manifolds and a classical way to compute it on compact complex manifolds is through the use of the associated spaces of harmonic forms. More precisely, if X is a complex manifold, then the exterior derivative d splits as ∂ + ∂̄ and such operators satisfy ∂̄ = ∂ = ∂∂̄ + ∂̄∂ = 0. Hence, one can define the Dolbeault cohomology and its conjugate as

[1]  P. Alam.  ‘N’ , 2021, Composites Engineering: An A–Z Guide.

[2]  Jonas Stelzig,et al.  Maximally non-integrable almost complex structures: an $h$-principle and cohomological properties , 2021 .

[3]  Bott-Chern and ∂̄ Harmonic Forms on Almost Hermitian 4-Manifolds , 2021 .

[4]  Kodaira dimension of almost Kähler manifolds and curvature of the canonical connection , 2019, 1908.11328.

[5]  Adriano Tomassini,et al.  On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures , 2021, International Journal of Mathematics.

[6]  S. Yau,et al.  Cohomology and Hodge Theory on Symplectic Manifolds: III , 2009, 0909.5418.

[7]  Adriano Tomassini,et al.  Almost-complex invariants of families of six-dimensional solvmanifolds , 2021, Complex Manifolds.

[8]  Scott O. Wilson,et al.  Topological and geometric aspects of almost Kähler manifolds via harmonic theory , 2018, Selecta Mathematica.

[9]  P. Gauduchon.  La 1-forme de torsion d'une variété hermitienne compacte , 1984 .

[10]  Adriano Tomassini,et al.  Bott-Chern Laplacian on almost Hermitian manifolds , 2021 .

[11]  P. D. Bartolomeis,et al.  On formality of some symplectic manifolds , 2001 .

[12]  Daniele Angella,et al.  Variational Problems in Conformal Geometry , 2019, The Journal of Geometric Analysis.

[13]  Scott O. Wilson,et al.  Dolbeault cohomology for almost complex manifolds , 2018, 1809.01416.

[14]  F. Hirzebruch.  Some problems on differentiable and complex manifolds , 1954 .