*Article* **Almost Hermitian Identities**

### **Joana Cirici 1 and Scott O. Wilson 2,\***


Received: 30 July 2020; Accepted: 11 August 2020; Published: 13 August 2020

**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.

**Keywords:** almost Hermitian manifolds; Kähler identities; Lefschetz operator
