Differential operators on almost-Hermitian manifolds and harmonic forms

2019/09/14 by Tardini, Nicoletta, Tomassini, Adriano · 1 citation
#32Q60 #53C15 #53D05 #58A14 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.06569

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.

Cited by

• Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds

Related

• More Differential Operators on Almost Hermitian Manifolds
• On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
• On the spaces of (d+d^c)-harmonic forms and (d+d^Λ)-harmonic forms on almost Hermitian manifolds and complex surfaces
• Topological and geometric aspects of almost K "ahler manifolds via\n harmonic theory
• Kähler identities for almost complex manifolds