On the spaces of (d+d c )-harmonic forms and (d+d Λ )-harmonic forms on almost Hermitian manifolds and complex surfaces

• Lorenzo Sillari ^[1] ; Adriano Tomassini ^[2]
  1. [1] International School for Advanced Studies

     International School for Advanced Studies

     Trieste, Italia

     
  2. [2] University of Parma

     University of Parma

     Parma, Italia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 6, 2024, págs. 2371-2398
• Idioma: inglés
• DOI: 10.4171/RMI/1492
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• Resumen

  • In this paper, we study the spaces of (d+d c)-harmonic forms and of (d+d Λ)-harmonic forms, a natural generalization of the spaces of Bott–Chern harmonic forms (respectively, symplectic harmonic forms) from complex (respectively, symplectic) manifolds to almost Hermitian manifolds. We apply the same techniques to compact complex surfaces, computing their Bott–Chern and Aeppli numbers and their spaces of (d+d Λ)-harmonic forms. We give several applications to compact quotients of Lie groups by a lattice.