Almost Hermitian Identities

TL;DR

This paper extends classical Kähler identities to almost Hermitian manifolds by analyzing the local commutation relations between the Lefschetz operator and the exterior differential, leading to new global geometric insights.

Contribution

It generalizes the fundamental Kähler identities to the broader context of almost Hermitian manifolds, providing a new framework for their study.

Findings

Derived generalized almost Hermitian identities

Established new global results for almost Hermitian manifolds

Extended classical Kähler identities to a broader setting

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 K\"ahler identities to the setting of almost Hermitian manifolds, allowing for new global results for such manifolds.