Kähler identities for almost complex manifolds

2022/08/15 by Fernandez, Luis, Hosmer, Samuel
#32Q60 #53C15 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.07276

Abstract

We obtain a generalization, for a general compact almost complex manifold, of the well-known Kähler (or Hodge) identities for Kähler manifolds involving the commutators of the exterior differential and the Lefschetz operator and its adjoint. The main idea is to study the problem on the Clifford bundle via the Dirac operator, and then translate the results to the exterior bundle.

Related

• Almost Hermitian Identities
• More Differential Operators on Almost Hermitian Manifolds
• Topological and geometric aspects of almost K "ahler manifolds via\n harmonic theory
• Compatible almost complex structures on the Hard Lefschetz condition
• Differential operators on almost-Hermitian manifolds and harmonic forms