Curvature of left-invariant complex Finsler metric on Lie groups

Let $G$ be an even-dimensional connected real Lie group admitting a left-invariant complex structure $J$. Let $\mathfrak g$ be the Lie algebra of $G$, and $\mathfrak g^{1,0}$ the $(1,0)$-part of the complexification $\mathfrak g^{\mathbb{C}}$ of $\mathfrak g$. We derive explicit formulas for the hol