Almost Hermitian Identities

2020/08/10 by Cirici, Joana, Wilson, Scott O.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.04390

Abstract

We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local Kähler identities to the setting of almost Hermitian manifolds, allowing for new global results for such manifolds.

Related

• Kähler identities for almost complex manifolds
• The hard Lefschetz duality for locally conformally almost Kähler manifolds
• More Differential Operators on Almost Hermitian Manifolds
• Differential operators on almost-Hermitian manifolds and harmonic forms
• Curvature identities on almost Hermitian manifolds and applications