Differential operators on almost-Hermitian manifolds and harmonic forms

Abstract

We consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces of harmonic forms and cohomologies with the classical de Rham, Dolbeault, Bott-Chern and Aeppli cohomologies.

Keywords

• almost-complex manifold
• almost-kähler manifold
• differential operator
• cohomology
• 32q60
• 53c15
• 58a14
• 53d05