On a class of almost Hermitian 4-manifolds

Abstract

Using an integral identity proved by Sekigawa \cite{Sek87} on compact almost Hermitian 4-manifolds, we naturally obtain a global characterization of the class ${\mathcal{A}\mathcal{H}}_1$ of almost Hermitian 4-manifolds satisfying the first Gray curvature condition from apparently weaker conditions. Then we take steps towards a classification of almost Hermitian 4-manifolds of class ${\mathcal{A}\mathcal{H}}_1$, including proving a uniqueness result on 4-dimensional Lie algebras.

26 pages, comments are welcome