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

• Andrea Cattaneo ^[1] ; Nicoletta Tardini ^[1] ; Adriano Tomassini ^[1]
  1. [1] University of Parma

     University of Parma

     Parma, Italia

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 1, 2024, págs. 301-316
• Idioma: inglés
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• Resumen

  • 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.