2 removed geometric analysis as a tag, since the result is most likely algebraic.
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# How to deduce this equation for a 4-dim almost Kahler manifold?

Let $(X,\omega,J)$ be a 4-dim almost Kahler manifold, equivalently, $(X,\omega)$ is an 4-dim symplectic manifold, $J$ is an almost complex structure on $X$ which is compatible with $\omega$, $g$ is the Riemann metric $\omega(X,Y)=g(JX,Y)$.

Denote $D$ to be the Levi-Civita connection which is compatible with $g$.

A $(0,2)$-tensor $B$ is defined by $B_{ij}=g^{kl}g_{mn}D_kJ_i^m D_lJ_j^n$.

I want to know how to deduce the equation $B=\frac{1}{4}|DJ|^2 g$ under the conditions given above?

REMARK: It seems that the condition '$X$ is 4-dim' is crucial.